## Taiwanese Journal of Mathematics

### NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION

X. H. Tang

#### Abstract

We consider the boundary value problem $$\tag{0.1} \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ & x\in \Omega,\\ u=0, \ \ \ \ & x\in \partial\Omega, \end{array} \right.$$ 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.

#### Article information

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

Dates
First available in Project Euclid: 21 July 2017

https://projecteuclid.org/euclid.twjm/1500667506

Digital Object Identifier
doi:10.11650/tjm.18.2014.3541

Mathematical Reviews number (MathSciNet)
MR3284041

Zentralblatt MATH identifier
1357.35163

#### Citation

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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