Multiple solutions for a class of singular quasilinear problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

dos Santos, Gelson¹  Figueiredo, Giovany M.²  Severo, Uberlandio B.³ 

[1] Univ Fed Para, Fac Matemat, BR-66075110 Belem, Para, Brazil

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

[3] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

关键词: Quasilinear operator;    Sub-supersolution method;    Singular problem;   

DOI  :  10.1016/j.jmaa.2019.123405

来源: Elsevier

【 摘 要 】

In this paper we use sub-supersolution and minimax methods to show the existence and multiplicity of solutions for the following class of singular quasilinear problems: {-Delta u - Delta(u(2))u = a(x)u(-beta) + h(x, u) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega is a bounded smooth domain of R-N (N >= 3), the function a(x) is nonnegative, beta > 0 is a constant and the nonlinearity h(x, u) is continuous. In our first result, the nonlinearity h has an arbitrary polynomial growth and we obtain the existence of a solution for the problem via sub-supersolution method. For the second result, h has subcritical growth and we show the existence of a second solution by applying the Mountain Pass Theorem. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free