Multi-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions
نویسنده
چکیده
In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + 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) satisfies some superlinear growth conditions and need not be odd or increasing strictly in t. 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 m−bump solutions for any positive integer m ≥ 2.
منابع مشابه
Multiple solutions of a Schrödinger type semilinear equation
Two nontrivial solutions are obtained for nonhomogeneous semilinear Schrödinger equations.
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