Multiple solutions for a class of singular quasilinear problems

[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.

[发布日期] 2019-12-15

[关键词] Quasilinear operator;Sub-supersolution method;Singular problem