Multi-bump solutions for a strongly indefinite semilinear Schrödinger equation without symmetry or convexity assumptions Original Research Article

In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: View the MathML source−Δu+V(x)u=f(x,u),u∈H1(RN). Turn MathJax on 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.