A variational approach to discontinuous problems with critical Sobolev exponents

被引：35

作者：

Alves, CO ^{[1
]}

Bertone, AM

Goncalves, JV

机构：

[1] Univ Fed Paraiba, Dept Matemat & Estat, Campina Grande, PB, Brazil

[2] Univ Fed Paraiba, Dept Matemat, BR-58059900 Joao Pessoa, Paraiba, Brazil

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 265卷 / 01期

关键词：

positive solutions; variational methods; critical Sobolev exponents; discontinuous nonlinearities;

D O I：

10.1006/jmaa.2001.7698

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form -Deltau = lambdah(x)H(u - a)u(q) + u(2*-1) in R-N, where lambda, a > 0 are parameters, h(x) is both nonnegative and integrable on R-N, H is the Heaviside function, 2* is the critical Sobolev exponent, and 0 less than or equal to q < 2* - 1. We obtain existence, multiplicity and regularity of solutions by distinguishing the cases 0 less than or equal to q less than or equal to 1 and 1 < q < 2*- 1. (C) 2002 Elsevier Science.

引用

页码：103 / 127

页数：25

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