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NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION

X. H. Tang
Taiwanese Journal of Mathematics
Vol. 18, No. 6 (December 2014), pp. 1957-1979
Stable URL: http://www.jstor.org/stable/taiwjmath.18.6.1957
Page Count: 23
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NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION
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Abstract

Abstract We consider the boundary value problem (0.1){−Δu+V(x)u=f(x, u),x∈Ω,u=0,x∈∂Ω, where Ω ⊂ ℝN is a bounded domain, infoΩV(x) > −∞, 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 Nehari-Pankov 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 Nehari-Pankov manifold by using the diagonal method. 2010 Mathematics Subject Classification: 35J20, 35J60. Key words and phrases: Schrödinger equation, Strongly indefinite functional, Superlinear, Diagonal method, Boundary value problem, Ground state solutions of Nehari-Pankov type.

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