What question did this study set out to answer?

The study aims to prove the existence of solutions for a particular class of nonlinear degenerate elliptic equations.

February 9, 2026Open Access

Existence of solutions for nonlinear degenerate elliptic equations with Lm-data and Neumann boundary condition

Key Points

The study aims to prove the existence of solutions for a particular class of nonlinear degenerate elliptic equations.
Analysis of a homogeneous Neumann elliptic problem
Application of distribution theory in proving existence
Utilization of anisotropic Sobolev spaces for function space framework
Existence of solutions in the sense of distributions is established
Findings pertain to bounded open domains with Lipschitz boundaries

Abstract

In this paper we consider the following homogenous Neumann elliptic problem cases -₈=₁^N Dⁱ (aᵢ (x, u, u) ) + ₈=₁^N A (|u|) Dⁱ u^pᵢ + |u|^p₀-2u = f in, \\ ₈=₁^N aᵢ (x, u, u) nᵢ = 0 on, cases where is a bounded open domain in RN (N 2) with Lipschitz boundary, we prove the existence of solutions in the sense of distributions for our elliptic problem in the anisotropic Sobolev spaces.

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Cite This Study

Badr et al. (Wed,) studied this question.

synapsesocial.com/papers/698979b9f0ec2af6756e79e7 https://doi.org/https://doi.org/10.2298/fil2516553b

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