Abstract
We consider a boundary value problem for p-Laplacian systems with two singular and subcritical nonlinearities. We obtain one theorem which shows that there exists at least one nontrivial weak solution for these problems under some conditions. We obtain this result by variational method and critical point theory.
Highlights
Let Ω be a bounded domain of Rn with smooth boundary ∂Ω, n ≥ 2
Let G be an open subset in R2 with compact complement C1 ∪ C2 = Rn \ G containing θ = (0, 0) and e = (e1, e2), where θ = (0, 0) ∈ C1 and e = (e1, e2) ∈ C2, n ≥ 2
In this paper we investigate existence and multiplicity of the solutions (u, v) ∈ W 1,p(Ω, G) for the p-Laplacian system with two singular and subcritical nonlinearities under the Dirichlet boundary condition:
Summary
Let Ω be a bounded domain of Rn with smooth boundary ∂Ω, n ≥ 2. Let G be an open subset in R2 with compact complement C1 ∪ C2 = Rn \ G containing θ = (0, 0) and e = (e1, e2), where θ = (0, 0) ∈ C1 and e = (e1, e2) ∈ C2, n ≥ 2. In this paper we investigate existence and multiplicity of the solutions (u, v) ∈ W 1,p(Ω, G) for the p-Laplacian system with two singular and subcritical nonlinearities under the Dirichlet boundary condition:. Singular problems involving p-Laplacian arise in applications of non-Newtonian fluid theory or the turbulent flow of a gas in a porous medium (cf [12, 19]). Our problems are characterized as a singular elliptic system with singular nonlinearities at {(u, v) = θ } and
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