Article ID Journal Published Year Pages File Type
844243 Nonlinear Analysis: Theory, Methods & Applications 2008 36 Pages PDF
Abstract

In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −Δu+V(x)u=f(x,u),u∈H1(RN). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x,t)f(x,t) satisfies some superlinear growth conditions and need not be odd or increasing in tt. Using a new variational reduction method and a generalized Morse theory, we proved that this equation has infinitely many geometrically different solutions. Furthermore, if the solutions of this equation under some energy level are isolated, then we can show that this equation has infinitely many mm-bump solutions for any positive integer m≥2m≥2.

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