Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient
We deal with the existence of constant sign solutions for the following variable exponent system Neumann boundary value problem: -div(|∇u|p(x)-2∇u)+λ|u|p(x)-2u=Fu(x,u,v) in Ω, -div(|∇v|q(x)-2∇v)+λ|v|q(x)-2v=Fv(x,u,v) in Ω, ∂u/∂γ=0=∂v/∂γ on ∂Ω. We give several sufficient conditions for the existe...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/396704 |
| Summary: | We deal with the existence of constant sign solutions for the following variable exponent system Neumann boundary value problem: -div(|∇u|p(x)-2∇u)+λ|u|p(x)-2u=Fu(x,u,v) in Ω, -div(|∇v|q(x)-2∇v)+λ|v|q(x)-2v=Fv(x,u,v) in Ω, ∂u/∂γ=0=∂v/∂γ on ∂Ω. We give several sufficient conditions for the existence of the constant sign solutions, when F(x,·,·) satisfies neither sub-(p(x),q(x)) growth condition, nor Ambrosetti-Rabinowitz condition (subcritical). In particular, we obtain the existence of eight constant sign solutions. |
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| ISSN: | 1085-3375 1687-0409 |