Positive Solutions for Semilinear Elliptic Equations: Two Simple Models with Several Bifurcations
β Scribed by Matteo Franca
- Publisher
- Springer US
- Year
- 2010
- Tongue
- English
- Weight
- 812 KB
- Volume
- 23
- Category
- Article
- ISSN
- 1040-7294
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π SIMILAR VOLUMES
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.
In this paper, we consider the semilinear elliptic equation For p=2NΓ(N&2), we show that there exists a positive constant +\\*>0 such that (V) + possesses at least one solution if + # (0, +\\*) and no solutions if +>+\\*. Furthermore, (V) + possesses a unique solution when +=+\\*, and at least two s
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.