The existence and multiplicity of positive solutions are obtained for a class of semilinear elliptic equations with critical weighted Hardy-Sobolev exponents and the concaveconvex nonlinearity by variational methods and some analysis techniques.
Positive solutions to a semilinear elliptic equation with a Sobolev–Hardy term
✍ Scribed by Ali Al-aati; Chunhua Wang; Jing Zhao
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 281 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0362-546X
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📜 SIMILAR VOLUMES
## Abstract In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with Hardy–Sobolev critical growth and singular term by using variation
Some existence and multiplicity results are obtained for solutions of semilinear elliptic equations with Hardy terms, Hardy-Sobolev critical exponents and superlinear nonlinearity by the variational methods and some analysis techniques.
In this paper, Neumann problem for nonlinear elliptic equations with critical Sobolev exponents and Hardy terms is studied by variational method. Based on the variant of the mountain pass theorem of Ambrosetti and Rabinowitz without (PS) condition, we prove the existence of positive solutions.