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Neumann problem with a discontinuous nonlinearity

Debajyoti Choudhuri, Dušan D. Repovš, Kamel Saoudi

Abstract

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive an estimate that proves the well-posedness of the problem. This estimate serves as an evidence for the uniqueness of the existing solution when the boundary term is ``smooth".

Neumann problem with a discontinuous nonlinearity

Abstract

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive an estimate that proves the well-posedness of the problem. This estimate serves as an evidence for the uniqueness of the existing solution when the boundary term is ``smooth".
Paper Structure (5 sections, 11 theorems, 64 equations)

This paper contains 5 sections, 11 theorems, 64 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Auxiliary Results
  4. Proofs of Main Results
  5. An Example

Key Result

Theorem 1.1

Assume that conditions C1-C3 are satisfied. Then the boundary value problem possesses infinitely many distinct solutions.

Theorems & Definitions (25)

  • Theorem 1.1
  • Theorem 1.2
  • Remark 1.3
  • Remark 1.4
  • Theorem 1.5
  • Conjecture 1.6
  • Conjecture 1.7
  • Definition 2.1
  • Theorem 2.2
  • Proposition 2.3
  • ...and 15 more