Let β R N be a smooth bounded domain such that 0 β , N 3, 0 s < 2, 2 \* (s) := 2(N - s)/N -2 is the critical Sobolev-Hardy exponent, f (x) is a given function. By using the Ekeland's variational principle and the mountain pass lemma, we prove the existence of multiple solutions for the singular crit
Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential
β Scribed by Daomin Cao; Shusen Yan
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 334 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0944-2669
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π SIMILAR VOLUMES
Let Ξ© β R N (N β₯ 3) be a smooth bounded domain such that the different points , are the critical Sobolev-Hardy exponents. We deal with the conditions that ensure the existence of positive solutions for the multi-singular and multi-critical elliptic problem with the Dirichlet boundary condition, in
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.
We consider the following problem, where ΞΌ > 0 is a large parameter, Ξ© is a bounded domain in R N , N 3 and 2 \* = 2N/(N -2). Let H (P ) be the mean curvature function of the boundary. Assuming that H (P ) has a local minimum point with positive minimum, then for any integer k, the above problem ha