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摘要: |
本文利用变分法,基于Lusternik-Schnirelmann畴数理论,讨论了一类关于算子$-\textup{div}(|x|^{-ap}|\nabla \cdot|^{p-2}\nabla \cdot)-\lambda\frac{|\cdot|^{p-2}\cdot}{|x|^{p(a+1)}}$的带权拟线性椭圆方程正解的多重性. |
关键词: 次临界Sobolev-Hardy指标,Nehari 流形,变号位势,凸凹非线性项 |
DOI: |
分类号:35J20; 35J75 |
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目) |
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Multiplicity of positive solutions for quasi-linear elliptic equations involving concave-convex nonlinearity and Sobolev-Hardy term |
duming
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Abstract: |
In this paper we investigate the multiple positive solutions of weighted quasi-linear elliptic equations for the operator $-\textup{div}(|x|^{-ap}|\nabla \cdot|^{p-2}\nabla \cdot)-\lambda\frac{|\cdot|^{p-2}\cdot}{|x|^{p(a+1)}}$ via variational methods and the theory of Lusternik-Schnirelmann category. |
Key words: subcritical Sobolev-Hardy exponent, Nehari manifold, sign-changing weight, concave-convex nonlinearity |