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Статті в журналах з теми "Semilinear Schrodinger equations"
Oliver, Marcel, and Claudia Wulff. "Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 3 (May 16, 2014): 603–36. http://dx.doi.org/10.1017/s0308210512002028.
Повний текст джерелаTarasov, V. O. "The integrable initial-boundary value problem on a semiline: nonlinear Schrodinger and sine-Gordon equations." Inverse Problems 7, no. 3 (June 1, 1991): 435–49. http://dx.doi.org/10.1088/0266-5611/7/3/009.
Повний текст джерелаДисертації з теми "Semilinear Schrodinger equations"
Secchi, Simone. "Nonlinear Differential Equations on Non-Compact Domains." Doctoral thesis, SISSA, 2002. http://hdl.handle.net/20.500.11767/4312.
Повний текст джерелаOliveira, Junior José Carlos de. "Equações elípticas semilineares e quasilineares com potenciais que mudam de sinal." reponame:Repositório Institucional da UnB, 2015. http://dx.doi.org/10.26512/2015.09.T.20199.
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Neste trabalho, consideramos o problema autônomo {(-∆u+V(x)u=f(u) em R^N,@u∈H^1 (R^N)\\{0},)┤ em que N≥3, a função V é não periódica, radialmente simétrica e muda de sinal e a não linearidade f é assintoticamente linear. Além disso, impomos que V possui um limite positivo no infinito e que o espectro do operador L≔-∆+V tem ínfimo negativo. Sob essas condições, baseando-se em interações entre soluções transladadas do problema no infinito associado, é possível mostrar que tal problema satisfaz a geometria do teorema de linking clássico e garantir a existência de uma solução fraca não trivial. Em seguida, estabelecemos a existência de uma solução não trivial para o problema não autônomo {(-∆u+V(x)u=f(x,u) em R^N,@u∈H^1 (R^N)\\{0},)┤ sob hipóteses similares ao problema anterior, admitindo também que f(x,u)=f(|x|,u) dentre outras condições. Aplicamos novamente o teorema de linking para garantir que tal problema possui uma solução não trivial. Por fim, provamos que o problema quasilinear {(-∆u+V(x)u-u∆(u^2)=g(x,u) em R^3,@u∈H^1 (R^3)\\{0},)┤ em que o potencial V muda de sinal, podendo ser não limitado inferiormente, e a não linearidade g(x,u), quando |x|→∞, possui um certo tipo de monotonicidade, possui uma solução não trivial. A existência de tal solução é provada por meio de uma mudança de variável que transforma o problema num problema semilinear, nos permitindo, assim, empregar o teorema do passo da montanha combinado com o lema splitting.
In this work, we consider the autonomous problem {(-∆u+V(x)u=f(u) em R^N,@u∈H^1 (R^N)\\{0},)┤ where N≥3, V is a non-periodic radially symmetric function that changes sign and the nonlinearity f is asymptotically linear. Furthermore, we impose that V has a positive limit at infinity and the spectrum of the operator L≔-∆+V has negative infimum. Under these conditions, employing interaction between translated solutions of the problem at infinity, it is possible to show that such problem satisfies the geometry of the classical linking theorem and garantee the existence of a nontrivial weak solution. After that, we establish the existence of a nontrivial weak solution for the nonautonomous problem {(-∆u+V(x)u=f(x,u) em R^N,@u∈H^1 (R^N)\\{0},)┤ under similar hyphoteses to the previous problem, assuming also that f(x,u)=f(|x|,u) among others conditions. We apply again the classical linking theorem to ensure that such problem possesses a nontrivial weak solution. Finally, we prove that the quasilinear problem {(-∆u+V(x)u-u∆(u^2)=g(x,u) em R^3,@u∈H^1 (R^3)\\{0},)┤ where the potential V changes sign and may be unbounded from below and the nonlinearity g(x,u), as|x|→∞, has a kind of monotonicity, has a nontrivial weak solution. The existence of such solution is proved by means of a change of variables that makes the problem become a semilinear problem and hence allow us apply the mountain pass theorem combined with splitting lemma.
Книги з теми "Semilinear Schrodinger equations"
Cazenave, Thierry. Semilinear Schrodinger Equations (Courant Lecture Notes). Courant Institute of Mathemetical Sciences, 2003.
Знайти повний текст джерелаЧастини книг з теми "Semilinear Schrodinger equations"
"Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations, 263–84. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-42.
Повний текст джерела"Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations, 237–70. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-6.
Повний текст джерела"Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations, 129–32. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-25.
Повний текст джерела"Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations, 103–56. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-3.
Повний текст джерела