Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues
We study the degenerate semilinear elliptic systems of the form -div(h1(x)∇u)=λ(a(x)u+b(x)v)+Fu(x,u,v),x∈Ω,-div(h2(x)∇v)=λ(d(x)v+b(x)u)+Fv(x,u,v),x∈Ω,u|∂Ω=v|∂Ω=0, where Ω⊂RN(N≥2) is an open bounded domain with smooth boundary ∂Ω, the measurable, nonnegative diffusion coefficients h1, h2 are allowed...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/532430 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We study the degenerate semilinear elliptic systems of the form -div(h1(x)∇u)=λ(a(x)u+b(x)v)+Fu(x,u,v),x∈Ω,-div(h2(x)∇v)=λ(d(x)v+b(x)u)+Fv(x,u,v),x∈Ω,u|∂Ω=v|∂Ω=0, where Ω⊂RN(N≥2) is an open bounded domain with smooth boundary ∂Ω, the measurable, nonnegative diffusion coefficients h1, h2 are allowed to vanish in Ω (as well as at the boundary ∂Ω) and/or to blow up in Ω¯. Some multiplicity results of solutions are obtained for the degenerate elliptic systems which are near resonance at higher eigenvalues by the classical saddle point theorem and a local saddle point theorem in critical point theory. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |