Taiwanese Journal of Mathematics


X. H. Tang

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We consider the boundary value problem \begin{equation} \tag{0.1} \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \  & x\in \Omega,\\ u=0, \ \ \ \ & x\in \partial\Omega, \end{array} \right. \end{equation} where $ \Omega \subset \mathbb R^N$ be a bounded domain, $\inf_{\Omega}V(x)\gt -\infty$, $f$ is a superlinear, subcritical nonlinearity. Inspired by previous work of Szulkin and Weth (2009)) [21] and (2010) [22], we develop a more direct and simpler approach on the basis of one used in [21], to deduce weaker conditions under which problem (0.1) has a ground state solution of generalized Nehari type or infinity many nontrivial solutions. Unlike the Nehari manifold method, the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the generalized Nehari manifold by using the diagonal method.

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Taiwanese J. Math., Volume 18, Number 6 (2014), 1957-1979.

First available in Project Euclid: 21 July 2017

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Primary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations

Schrödinger equation strongly indefinite functional superlinear diagonal method boundary value problem ground state solutions of Nehari-Pankov type


Tang, X. H. NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION. Taiwanese J. Math. 18 (2014), no. 6, 1957--1979. doi:10.11650/tjm.18.2014.3541. https://projecteuclid.org/euclid.twjm/1500667506

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