期刊
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
卷 60, 期 3, 页码 -出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-021-01963-1
关键词
-
资金
- National Natural Science Foundation of China [11971485, 12001542]
This paper presents a direct approach to finding nontrivial solutions and ground state solutions for a specific planar Schrodinger equation, while extending and improving upon previous results from related studies.
In the present paper, we develop a direct approach to find nontrivial solutions and ground state solutions for the following planar Schrodinger equation: {- Delta u + V(x)u = f ( x, u), x is an element of R-2, u is an element of H-1(R-2), where V(x) is an 1-periodic function with respect to x(1) and x(2), 0 lies in a gap of the spectrum of - Delta + V, and f ( x, t) behaves like +/- e(proportional to t2) as t -> +/- infinity uniformly on x is an element of R-2. Our theorems extend and improve the results of de Figueiredo-Miyagaki-Ruf (Calc Var Partial Differ Equ, 3(2):139-153, 1995), of de Figueiredo-do O-Ruf (Indiana Univ Math J, 53(4):1037-1054, 2004), of Alves-Souto-Montenegro (Calc Var Partial Differ Equ 43: 537-554, 2012), of Alves-Germano (J Differ Equ 265: 444-477, 2018) and of do O-Ruf (NoDEA 13: 167-192, 2006).
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