On a semilinear Schrödinger equation with critical Sobolev exponent期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On a semilinear Schrödinger equation with critical Sobolev exponent

Authors:	Jan Chabrowski Andrzej Szulkin

Institution:	Department of Mathematics, University of Queensland, St. Lucia 4072, Queensland, Australia ; Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden

Abstract:	We consider the semilinear Schrödinger equation $-\Delta u+V(x)u = K(x)\vert u\vert^{2^{*}-2}u+g(x,u)$ , $u\in W^{1,2}(\mathbf{R}^{N})$ , where $N\ge 4$ , are periodic in $x_{j}$ for $1\le j\le N$ , , is of subcritical growth and 0 is in a gap of the spectrum of $-\Delta+V$ . We show that under suitable hypotheses this equation has a solution $u\ne 0$ . In particular, such a solution exists if $K\equiv 1$ and $g\equiv 0$ .

Keywords:	Semilinear Schr\"odinger equation critical Sobolev exponent linking

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