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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/532430 |
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| author | Yu-Cheng An Hong-Min Suo |
| author_facet | Yu-Cheng An Hong-Min Suo |
| author_sort | Yu-Cheng An |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-eb9fb408a4fc4d99bce9eaa27f307d4e |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-eb9fb408a4fc4d99bce9eaa27f307d4e2025-08-20T02:22:20ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/532430532430Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher EigenvaluesYu-Cheng An0Hong-Min Suo1School of Sciences, Guizhou Minzu University, Guiyang 550025, ChinaSchool of Sciences, Guizhou Minzu University, Guiyang 550025, ChinaWe 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.http://dx.doi.org/10.1155/2012/532430 |
| spellingShingle | Yu-Cheng An Hong-Min Suo Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues Abstract and Applied Analysis |
| title | Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues |
| title_full | Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues |
| title_fullStr | Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues |
| title_full_unstemmed | Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues |
| title_short | Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues |
| title_sort | multiple solutions for degenerate elliptic systems near resonance at higher eigenvalues |
| url | http://dx.doi.org/10.1155/2012/532430 |
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