A $p$-Laplacian system with resonance and nonlinear boundary conditions on an unbounded domain

Dimitrios A. Kandilakis; Manolis Magiropoulos

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The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the $N$ -Laplacian $- Δ_{N} u \equiv - {div (| \nabla u |}^{N - 2} \nabla u) = e (x, u) + h (x) in Ω$ where $u \in W_{0}^{1, N} (ℝ^{N})$ , $Ω$ is a bounded smooth domain in $ℝ^{N}$ , $N \geq 2$ , $e (x, u)$ is a critical nonlinearity in the sense of the Trudinger-Moser inequality and $h (x) \in {(W_{0}^{1, N})}^{*}$ is a small perturbation.

Displaying similar documents to “A p -Laplacian system with resonance and nonlinear boundary conditions on an unbounded domain”

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Displaying similar documents to “A $p$ -Laplacian system with resonance and nonlinear boundary conditions on an unbounded domain”

Solutions to a perturbed critical semilinear equation concerning the $N$ -Laplacian in $ℝ^{N}$