Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity

Advances in Nonlinear Analysis

article

Xiangdong Fang¹  Jianjun Zhang² 

[1] School of Mathematical Sciences, Dalian University of Technology;College of Mathematics and Statistics, Chongqing Jiaotong University;Università degli Studi dell’Insubria

关键词: Quasilinear elliptic equation;    Positive solution;    Nehari manifold;   

DOI  :  10.1515/anona-2020-0058

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We are concerned with the following quasilinear elliptic equation − Δ u− Δ (u2)u=μ |u|q− 2u+|u|2⋅ 2∗ − 2u,u∈ H01(Ω ), $$\begin{array}{} \displaystyle -{\it\Delta} u-{\it\Delta}(u^{2})u=\mu |u|^{q-2}u+|u|^{2\cdot 2^*-2}u, u\in H_0^1({\it\Omega}), \end{array}$$(QSE) where Ω ⊂ ℝ N is a bounded domain, N ≥ 3, q N 0 such that (QSE) admits at least cat Ω ( Ω ) positive solutions when μ ∈ (0, μ * ).

【 授权许可】

CC BY