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Afrouzi, G. A.
- On the Existence, Nonexistence and Uniqueness of Positive Weak Solutions for Nonlinear Multiparameter Elliptic Systems Involving the (P,Q)-Laplacian
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Authors
Affiliations
1 Department of Mathematics, Babol University of Technology, Babol, IR
2 Department of Mathematics, University of Mazandaran, Babolsar, IR
1 Department of Mathematics, Babol University of Technology, Babol, IR
2 Department of Mathematics, University of Mazandaran, Babolsar, IR
Source
The Journal of the Indian Mathematical Society, Vol 78, No 1-4 (2011), Pagination: 163-172Abstract
The paper deal with the existence, nonexistence and uniqueness of positive weak solutions for the nonlinear multiparameter elliptic system
{ −Δpu = λ1 f(v) + μ1 h(u); x∈Ω, −Δqv = λ2 g(u) + μ2 k(v); x ∈ Ω, u=0=v; x ∈ ∂Ω,
where Ω is a bounded domain in RN(N > 1) with smooth boundary ∂Ω, Δp denotes the p-Laplacian operator defined by Δpz = div (|∇z|p-2∇z), p>1,f, g, h, k: [0,∞) → [0,∞), and λ1, λ2, μ1,μ2 are positive parameters. A positive weak solution is obtained by applying the Schauder Fixed Point Theorem, together with comparison principles for the p-Laplacian. A uniqueness and nonexistence result is also obtained.