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On superlinear Schrödinger equations with periodic potential. (English) Zbl 1247.35149
Summary: We obtain ground state solutions for a wide class of superlinear Schrödinger equations with periodic potential. The result improves the recent result of A. Szulkin and T. Weth [J. Funct. Anal. 257, No. 12, 3802–3822 (2009; Zbl 1178.35352)]. The main ingredient is the observation that even in the strongly indefinite case, all Cerami sequences for the energy functional are bounded.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35J65 Nonlinear boundary value problems for linear elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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