Two positive solutions for quasilinear elliptic equations with singularity and critical exponents

作者：Sang, Yanbin^*; Luo, Xiaorong; Zhu, Zongyuan

来源：Boundary Value Problems, 2018, 2018(1): 97.

DOI：10.1186/s13661-018-1018-7

• Quasilinear
• Singularity
• Critical
• Sobolev-Hardy exponent

In this paper, we consider the quasilinear elliptic equation with singularity and critical exponents @@@ {-Delta(p)u - mu vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(p) = Q(X) vertical bar u vertical bar(p)*(()t)(-2)u/vertical bar x vertical bar t + lambda u(-s), in Omega, @@@ u > 0, in Omega, @@@ u = 0, on partial derivative Omega, @@@ where Delta p = div(vertical bar del u vertical bar(p- 2) del u) is a p- Laplace operator with 1 < p < N. p*(t) := p(N- t)/N-p is a critical Sobolev- Hardy exponent. We deal with the existence of multiple solutions for the above problem by means of variational and perturbation methods.

• 出版日期2018-6-22
• 单位浙江财经大学; 中北大学