We use bifurcation theory to study positive, negative, and sign-changing solutions for several classes of boundary value problems, depending on a real parameter . We show the existence of infinitely many points of pitchfork bifurcation, and study global properties of the solution curves.
On the uniqueness of solution for a class of semilinear elliptic problems
✍ Scribed by D.G Costa; D.G de Figueiredo; J.V.A Gonçalves
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 517 KB
- Volume
- 123
- Category
- Article
- ISSN
- 0022-247X
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📜 SIMILAR VOLUMES
We discuss the existence of multiple solutions of nonlinear elliptic equations by a combination of variational, topological methods and the generalized Conley index theory. We obtain several positive solutions and sign-changing solutions. Our main point is to show the usefulness of the Morse inequal
Ž . Ž . decays to zero near ϱ provided H t t dt -ϱ, where t s max p x . Fur-0 < x <st thermore, they show that this condition on p is nearly optimal.
The existence and multiplicity results are obtained for solutions of a class of the Dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods, respectively.