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We study the nonexistence, existence and multiplicity of positive solutions for the nonlinear Neumann boundary value problem involving the p(x)-Laplacian of the form {−Δp(x)u+λ|u|p(x)−2u=f(x,u)in Ω|∇u|p(x)−2∂u∂η=g(x,u)on ∂Ω, where Ω is a bounded smooth domain in RN, p∈C1(Ω¯) and p(x)>1 for x∈Ω¯. Using the sub–supersolution method and the variational principles, under appropriate assumptions on...
In this paper, using sub–supersolution method, we study the positive solution of the p(x)-Laplacian equations −Δp(x)u=f(x,u) with Dirichlet boundary condition on a bounded domain Ω in Rn with C1,ω¯ boundary for some 0<ω¯<1 for a possibly singular nonlinearity f on Ω×(0,∞).
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