Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues

Yu-Cheng An and Hong-Min Suo

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/532430

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:532430

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().