Positive and nodal solutions for an elliptic equation with critical growth

被引：9

作者：

Furtado, Marcelo F. ^{[1
]}

Souza, Bruno N. ^{[2
]}

机构：

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[2] Univ Fed Triangulo Mineiro, ICTE, BR-38064200 Uberaba, MG, Brazil

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2016年 / 18卷 / 02期

关键词：

Critical exponent; positive solution; nodal solution; elliptic equations; CRITICAL SOBOLEV EXPONENT; MULTIPLICITY; TOPOLOGY;

D O I：

10.1142/S0219199715500212

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem -div(p(x)del u) = lambda vertical bar u|(q-2)u + vertical bar u vertical bar(2*-2)u, u is an element of H-0(1)(Omega), where Omega subset of R-N is a bounded smooth domain, N >= 4, 2* = 2N/(N - 2), 2 <= q < 2*. Under some suitable conditions on the continuous potential p(x) and on the parameter lambda > 0, we obtain one nodal solution for q = 2 and one positive solution for 2 < q < 2*.

引用

页数：16

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