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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.

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
Full Text: DOI
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