The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions
β Scribed by Tsung-Fang Wu
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 253 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
We use the mountain pass theorem to study the existence and multiplicity of positive solutions of the generalisation of the well-known logistic equation -u = g(x)u(x)(1 -u(x)) with Dirichlet boundary conditions to the case where g changes sign.
The existence and multiplicity of weak solutions is established for a class of concave-convex elliptic systems of the form: R 2 \ {(0, 0)}, the weight m(x) is a positive bounded function and a(x), b(x) β C (β¦) are functions which change sign in β¦. Our technical approach is based on the Nehari manifo
A p-Laplacian system with Dirichlet boundary conditions is investigated. By analysis of the relationship between the Nehari manifold and fibering maps, we will show how the Nehari manifold changes as Ξ», Β΅ varies and try to establish the existence of multiple positive solutions.