New conditions on nonlinearity for a periodic Schrodinger equation having zero as spectrum

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Tang, X. H.

关键词: Schrodinger equation;    Zero spectrum point;    Superlinear;    Ground state solutions;   

DOI  :  10.1016/j.jmaa.2013.11.062

来源: Elsevier

【 摘 要 】

We consider the semilinear Schrodinger equation {-Delta u + V(x)u = f(x, u), for x is an element of R-N, u(x) -> 0, as vertical bar x vertical bar -> infinity, where f is a superlinear and subcritical nonlinearity. We mainly study the case when both V and f are periodic in x and 0 is a boundary point of a spectral gap of -Delta + V. We extend a linking theorem of Kryszewski and Szulkin [15] and establish a new variational setting which is more suitable to the above case. We obtain two theorems on the existence of ground state solutions with mild assumptions on f. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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