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Published: 14 March 2023

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1

Manning, Robert S. "Conjugate Points Revisited and Neumann–Neumann Problems." SIAM Review 51, no. 1 (February 5, 2009): 193–212. http://dx.doi.org/10.1137/060668547.

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2

Szajewska, Marzena, and Agnieszka Tereszkiewicz. "TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS." Acta Polytechnica 56, no. 3 (June 30, 2016): 245. http://dx.doi.org/10.14311/ap.2016.56.0245.

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Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.
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3

Gasiński, Leszek, Liliana Klimczak, and Nikolaos S. Papageorgiou. "Nonlinear noncoercive Neumann problems." Communications on Pure and Applied Analysis 15, no. 4 (April 2016): 1107–23. http://dx.doi.org/10.3934/cpaa.2016.15.1107.

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4

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Anisotropic nonlinear Neumann problems." Calculus of Variations and Partial Differential Equations 42, no. 3-4 (January 19, 2011): 323–54. http://dx.doi.org/10.1007/s00526-011-0390-2.

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5

Motreanu, D., V. V. Motreanu, and N. S. Papageorgiou. "On resonant Neumann problems." Mathematische Annalen 354, no. 3 (December 23, 2011): 1117–45. http://dx.doi.org/10.1007/s00208-011-0763-z.

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6

Nittka, Robin. "Inhomogeneous parabolic Neumann problems." Czechoslovak Mathematical Journal 64, no. 3 (September 2014): 703–42. http://dx.doi.org/10.1007/s10587-014-0127-4.

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7

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Nonlinear Neumann Problems with Constraints." Funkcialaj Ekvacioj 56, no. 2 (2013): 249–70. http://dx.doi.org/10.1619/fesi.56.249.

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8

Motreanu, D., V. V. Motreanu, and N. S. Papageorgiou. "Nonlinear Neumann problems near resonance." Indiana University Mathematics Journal 58, no. 3 (2009): 1257–80. http://dx.doi.org/10.1512/iumj.2009.58.3565.

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9

Ferone, V., and A. Mercaldo. "Neumann Problems and Steiner Symmetrization." Communications in Partial Differential Equations 30, no. 10 (September 2005): 1537–53. http://dx.doi.org/10.1080/03605300500299596.

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10

Bramanti, Marco. "Symmetrization in parabolic neumann problems." Applicable Analysis 40, no. 1 (January 1991): 21–39. http://dx.doi.org/10.1080/00036819008839990.

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11

Aizicovici, Sergiu, Nikolaos S. Papageorgiou, and Vasile Staicu. "Nonlinear, nonhomogeneous parametric Neumann problems." Topological Methods in Nonlinear Analysis 48, no. 1 (April 24, 2016): 1. http://dx.doi.org/10.12775/tmna.2016.035.

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12

Candito, Pasquale, Roberto Livrea, and Nikolaos Papageorgiou. "Nonlinear nonhomogeneous Neumann eigenvalue problems." Electronic Journal of Qualitative Theory of Differential Equations, no. 46 (2015): 1–24. http://dx.doi.org/10.14232/ejqtde.2015.1.46.

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13

Cianchi, Andrea, and Vladimir G. Maz'ya. "Neumann problems and isocapacitary inequalities." Journal de Mathématiques Pures et Appliquées 89, no. 1 (January 2008): 71–105. http://dx.doi.org/10.1016/j.matpur.2007.10.001.

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14

Volzone, Bruno. "Symmetrization for fractional Neumann problems." Nonlinear Analysis: Theory, Methods & Applications 147 (December 2016): 1–25. http://dx.doi.org/10.1016/j.na.2016.08.029.

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15

Rachůnková, Irena, Svatoslav Staněk, Ewa Weinmüller, and Michael Zenz. "Neumann problems with time singularities." Computers & Mathematics with Applications 60, no. 3 (August 2010): 722–33. http://dx.doi.org/10.1016/j.camwa.2010.05.019.

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16

Dudko, Anastasia, and Vyacheslav Pivovarchik. "Three spectra problem for Stieltjes string equation and Neumann conditions." Proceedings of the International Geometry Center 12, no. 1 (February 28, 2019): 41–55. http://dx.doi.org/10.15673/tmgc.v12i1.1367.

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Spectral problems are considered which appear in description of small transversal vibrations of Stieltjes strings. It is shown that the eigenvalues of the Neumann-Neumann problem, i.e. the problem with the Neumann conditions at both ends of the string interlace with the union of the spectra of the Neumann-Dirichlet problems, i.e. problems with the Neumann condition at one end and Dirichlet condition at the other end on two parts of the string. It is shown that the spectrum of Neumann-Neumann problem on the whole string, the spectrum of Neumann-Dirichlet problem on the left part of the string, all but one eigenvalues of the Neumann-Dirichlet problem on the right part of the string and total masses of the parts uniquely determine the masses and the intervals between them.
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17

Qiu, Guohuan, and Chao Xia. "Classical Neumann Problems for Hessian Equations and Alexandrov–Fenchel’s Inequalities." International Mathematics Research Notices 2019, no. 20 (January 26, 2018): 6285–303. http://dx.doi.org/10.1093/imrn/rnx296.

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Abstract Recently, the 1st named author together, with Xinan Ma [12], has proved the existence of the Neumann problems for Hessian equations. In this paper, we proceed further to study classical Neumann problems for Hessian equations. We prove here the existence of classical Neumann problems for uniformly convex domains in $\mathbb {R}^{n}$. As an application, we use the solution of the classical Neumann problem to give a new proof of a family of Alexandrov–Fenchel inequalities arising from convex geometry. This geometric application is motivated by Reilly [18].
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18

Fiacca, Antonella, and Raffaella Servadei. "Extremal solutions for nonlinear neumann problems." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 21, no. 2 (2001): 191. http://dx.doi.org/10.7151/dmdico.1024.

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19

López, Ginés, and Juan-Aurelio Montero-Sánchez. "Neumann boundary value problems across resonance." ESAIM: Control, Optimisation and Calculus of Variations 12, no. 3 (June 20, 2006): 398–408. http://dx.doi.org/10.1051/cocv:2006009.

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20

Pomponio, Alessio. "Singularly perturbed Neumann problems with potentials." Topological Methods in Nonlinear Analysis 23, no. 2 (June 1, 2004): 301. http://dx.doi.org/10.12775/tmna.2004.013.

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21

Fan, Xianling. "Eigenvalues of the -Laplacian Neumann problems." Nonlinear Analysis: Theory, Methods & Applications 67, no. 10 (November 2007): 2982–92. http://dx.doi.org/10.1016/j.na.2006.09.052.

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22

Kristály, Alexandru. "Perturbed Neumann Problems with Many Solutions." Numerical Functional Analysis and Optimization 29, no. 9-10 (November 13, 2008): 1114–27. http://dx.doi.org/10.1080/01630560802418383.

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23

Papalini, Francesca. "Nonlinear eigenvalue Neumann problems with discontinuities." Journal of Mathematical Analysis and Applications 273, no. 1 (September 2002): 137–52. http://dx.doi.org/10.1016/s0022-247x(02)00222-6.

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24

Halidias, N. "Neumann boundary value problems with discontinuities." Applied Mathematics Letters 16, no. 5 (July 2003): 729–32. http://dx.doi.org/10.1016/s0893-9659(03)00074-0.

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25

Buttazzo, Giuseppe, and Franco Tomarelli. "Compatibility conditions for nonlinear Neumann problems." Advances in Mathematics 89, no. 2 (October 1991): 127–43. http://dx.doi.org/10.1016/0001-8708(91)90076-j.

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26

Hu, Shouchuan, and N. S. Papageorgiou. "Nonlinear elliptic problems of Neumann-type." Rendiconti del Circolo Matematico di Palermo 50, no. 1 (January 2001): 47–66. http://dx.doi.org/10.1007/bf02843918.

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27

Pan, Xing-Bin. "Singular limit of quasilinear Neumann problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 1 (1995): 205–23. http://dx.doi.org/10.1017/s0308210500030845.

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This paper is devoted to the study of the singular limit of the minimal solutions, as p → 1, of quasilinear Neumann problems involving p-Laplacian operators. It is established that the limit function is of bounded variation and is locally Höolder-continuous inside the domain.
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28

Filippakis, Michael, Leszek Gasiński, and Nikolaos S. Papageorgiou. "Multiplicity Results for Nonlinear Neumann Problems." Canadian Journal of Mathematics 58, no. 1 (February 1, 2006): 64–92. http://dx.doi.org/10.4153/cjm-2006-004-6.

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AbstractIn this paper we study nonlinear elliptic problems of Neumann type driven by the p-Laplacian differential operator. We look for situations guaranteeing the existence of multiple solutions. First we study problems which are strongly resonant at infinity at the first (zero) eigenvalue. We prove five multiplicity results, four for problems with nonsmooth potential and one for problems with a C1-potential. In the last part, for nonsmooth problems in which the potential eventually exhibits a strict super-p-growth under a symmetry condition, we prove the existence of infinitely many pairs of nontrivial solutions. Our approach is variational based on the critical point theory for nonsmooth functionals. Also we present some results concerning the first two elements of the spectrum of the negative p-Laplacian with Neumann boundary condition.
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29

Dipierro, Serena, Xavier Ros-Oton, and Enrico Valdinoci. "Nonlocal problems with Neumann boundary conditions." Revista Matemática Iberoamericana 33, no. 2 (2017): 377–416. http://dx.doi.org/10.4171/rmi/942.

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30

Taira, Kazuaki. "Logistic Neumann problems with discontinuous coefficients." ANNALI DELL'UNIVERSITA' DI FERRARA 66, no. 2 (September 18, 2020): 409–85. http://dx.doi.org/10.1007/s11565-020-00350-6.

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31

Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Neumann problems for nonlinear hemivariational inequalities." Mathematische Nachrichten 280, no. 3 (February 2007): 290–301. http://dx.doi.org/10.1002/mana.200410482.

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32

Serra, Enrico, and Paolo Tilli. "Monotonicity constraints and supercritical Neumann problems." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 28, no. 1 (January 2011): 63–74. http://dx.doi.org/10.1016/j.anihpc.2010.10.003.

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33

Vasilyev, Vladimir. "On the Dirichlet and Neumann problems in multi-dimensional cone." Mathematica Bohemica 139, no. 2 (2014): 333–40. http://dx.doi.org/10.21136/mb.2014.143858.

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34

Le Tallec, Patrick, Jan Mandel, and Marina Vidrascu. "A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems." SIAM Journal on Numerical Analysis 35, no. 2 (April 1998): 836–67. http://dx.doi.org/10.1137/s0036142995291019.

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35

Heinkenschloss, Matthias, and Hoang Nguyen. "Neumann--Neumann Domain Decomposition Preconditioners for Linear-Quadratic Elliptic Optimal Control Problems." SIAM Journal on Scientific Computing 28, no. 3 (January 2006): 1001–28. http://dx.doi.org/10.1137/040612774.

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36

Urquhart, Alasdair. "Von Neumann, Gödel and Complexity Theory." Bulletin of Symbolic Logic 16, no. 4 (December 2010): 516–30. http://dx.doi.org/10.2178/bsl/1294171130.

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AbstractAround 1989, a striking letter written in March 1956 from Kurt Gödel to John von Neumann came to light. It poses some problems about the complexity of algorithms; in particular, it asks a question that can be seen as the first formulation of the P = ? NP question. This paper discusses some of the background to this letter, including von Neumann's own ideas on complexity theory. Von Neumann had already raised explicit questions about the complexity of Tarski's decision procedure for elementary algebra and geometry in a letter of 1949 to J. C. C. McKinsey. The paper concludes with a discussion of why theoretical computer science did not emerge as a separate discipline until the 1960s.
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37

Dassios, G., and A. S. Fokas. "The basic elliptic equations in an equilateral triangle." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2061 (July 27, 2005): 2721–48. http://dx.doi.org/10.1098/rspa.2005.1466.

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In his deep and prolific investigations of heat diffusion, Lamé was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular, he derived explicit results for the Dirichlet and Neumann cases using an ingenious change of variables. The relevant eigenfunctions are a complicated infinite series in terms of his variables. Here we first show that boundary-value problems with simple boundary conditions, such as the Dirichlet and the Neumann problems, can be solved in an elementary manner. In particular, the unknown Neumann and Dirichlet boundary values can be expressed in terms of a Fourier series for the Dirichlet and the Neumann problems, respectively. Our analysis is based on the so-called global relation, which is an algebraic equation coupling the Dirichlet and the Neumann spectral values on the perimeter of the triangle. As Lamé correctly pointed out, infinite series are inadequate for expressing the solution of more complicated problems such as mixed boundary-value problems. In this paper we show, further utilizing the global relation, that such problems can be solved in terms of generalized Fourier integrals .
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38

Th. Kyritsi, Sophia, and Nikolaos S. Papageorgiou. "Multiple solutions for nonlinear coercive Neumann problems." Communications on Pure & Applied Analysis 8, no. 6 (2009): 1957–74. http://dx.doi.org/10.3934/cpaa.2009.8.1957.

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39

Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Nonlinear Neumann problems with asymmetric nonsmooth potential." Bulletin of the Belgian Mathematical Society - Simon Stevin 12, no. 3 (September 2005): 417–33. http://dx.doi.org/10.36045/bbms/1126195346.

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40

Jankowski, Tadeusz. "Existence and approximate solutions of Neumann problems." Integral Transforms and Special Functions 14, no. 5 (October 2003): 429–36. http://dx.doi.org/10.1080/1065246031000081625.

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41

Da Lio, Francesca, and Francesco Palmurella. "Remarks on Neumann boundary problems involving Jacobians." Communications in Partial Differential Equations 42, no. 10 (September 8, 2017): 1497–509. http://dx.doi.org/10.1080/03605302.2017.1377231.

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42

Alves, Claudianor O., and Abbas Moameni. "Super-critical Neumann problems on unbounded domains." Nonlinearity 33, no. 9 (July 23, 2020): 4568–89. http://dx.doi.org/10.1088/1361-6544/ab8bac.

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43

Willatzen, M., A. Pors, and J. Gravesen. "Strong curvature effects in Neumann wave problems." Journal of Mathematical Physics 53, no. 8 (August 2012): 083507. http://dx.doi.org/10.1063/1.4745856.

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44

Szymanska-Debowska, Katarzyna. "Solutions to nonlocal Neumann boundary value problems." Electronic Journal of Qualitative Theory of Differential Equations, no. 28 (2018): 1–14. http://dx.doi.org/10.14232/ejqtde.2018.1.28.

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45

Kristály, Alexandru, and Dumitru Motreanu. "Nonsmooth Neumann-Type Problems Involving thep-Laplacian." Numerical Functional Analysis and Optimization 28, no. 11-12 (December 10, 2007): 1309–26. http://dx.doi.org/10.1080/01630560701749698.

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46

Anoop, T. V., and Nirjan Biswas. "Neumann eigenvalue problems on the exterior domains." Nonlinear Analysis 187 (October 2019): 339–51. http://dx.doi.org/10.1016/j.na.2019.05.004.

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47

Papageorgiou, Nikolaos S., Ana Isabel Santos Coelho Rodrigues, and Vasile Staicu. "On resonant Neumann problems: Multiplicity of solutions." Nonlinear Analysis: Theory, Methods & Applications 74, no. 17 (December 2011): 6487–98. http://dx.doi.org/10.1016/j.na.2011.06.031.

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48

Dauge, Monique. "Neumann and mixed problems on curvilinear polyhedra." Integral Equations and Operator Theory 15, no. 2 (March 1992): 227–61. http://dx.doi.org/10.1007/bf01204238.

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49

Chu, Jifeng, Yigang Sun, and Hao Chen. "Positive solutions of Neumann problems with singularities." Journal of Mathematical Analysis and Applications 337, no. 2 (January 2008): 1267–72. http://dx.doi.org/10.1016/j.jmaa.2007.04.070.

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50

Bandle, Catherine, and Maria Assunta Pozio. "On a class of nonlinear Neumann problems." Annali di Matematica Pura ed Applicata 157, no. 1 (December 1990): 161–82. http://dx.doi.org/10.1007/bf01765317.

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