Minimal nodal solutions of a Schrodinger equation with critical nonlinearity and symmetric potential

Monica Clapp; Yanheng Ding

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Minimal nodal solutions of a Schrodinger equation with critical nonlinearity and symmetric potential

机译：具有临界非线性和对称势的薛定inger方程的最小节点解

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We study the nonlinear Schrodinger equation -△u + λa(x)u = μu+ u~(2~*-1), u ∈ R~N, with critical exponent 2~* = 2N/(N-2), N ≥ 4, where a ≥ 0 has a potential well and is invariant under an orthogonal involution of R~N. Using variational methods we establish existence and multiplicity of solutions which change sign exactly once. These solutions localize near the potential well for μ small and λ large.

机译：我们研究非线性Schrodinger方程-△u +λa（x）u =μu+ u〜（2〜* -1），u∈R〜N，临界指数2〜* = 2N /（N-2），N≥在图4中，a≥0具有势阱，并且在R〜N的正交对合下不变。使用变分方法，我们建立了正好改变一次符号的解的存在性和多重性。这些解决方案位于μ小和λ大的势阱附近。

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《Differential and integral equations》 |2003年第8期|共12页
作者
Monica Clapp; Yanheng Ding;
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正文语种 eng
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1. Minimal nodal solutions of a Schrodinger equation with critical nonlinearity and symmetric potential [J] . Monica Clapp, Yanheng Ding Differential and integral equations . 2003,第8期

机译：具有临界非线性和对称势的薛定inger方程的最小节点解
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3. Exact localized solutions of (1+1)-dimensional nonlinear Schrodinger equation with complex PT symmetric potentials and power-law nonlinearity [J] . Nath D., Roy P. Journal of nonlinear optical physics & materials . 2016,第3期

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Minimal nodal solutions of a Schrodinger equation with critical nonlinearity and symmetric potential

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