A NON-PERIODIC INDEFINITE VARIATIONAL PROBLEM IN RN WITH CRITICAL EXPONENT

被引：0

作者：

Costa, Gustavo S. Do Amaral ^{[1
]}

Figueiredo, Giovany M. M. ^{[2
]}

Junior, Jose Carlos D. E. O. ^{[3
]}

机构：

[1] Univ Fed Maranhao, Dept Matemat, Sao Luis, Brazil

[2] Univ Brasilia, Dept Matemat, Brasilia, DF, Brazil

[3] Univ Fed Norte Tocantins, Colegiado Matemat, Araguaina, Tocantins, Brazil

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2023年 / 66卷 / 02期

关键词：

critical exponent; abstract linking theorem; indefinite problems; spectral theory; SEMILINEAR SCHRODINGER-EQUATION; EXISTENCE;

D O I：

10.1017/S0013091523000330

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the non-linear Schrodinger equation -Delta u + V(x)u = mu integral(u)+vertical bar u vertical bar(2*-2)u, (P mu) in R-N, N >= 3, where V changes sign and f (s)/s, s not equal 0, is bounded, with V non-periodic in x. The existence of a solution is established employing spectral theory, a general linking theorem due to [12] and interaction between translated solutions of the problem at infinity with some qualitative properties of them.

引用

页码：579 / 612

页数：34

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