On a doubly sublinear fractional p-Laplacian equation

2024/09/05 by Antonio Iannizzotto, Sunra Mosconi, Iannizzotto, A. +1 · 2 citations
Mathematics · #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.2409.03616

Abstract

We prove a bifurcation result for a Dirichlet problem driven by the fractional p-Laplacian (either degenerate or singular), in which the reaction is the difference between two sublinear powers of the unknown. In our argument, a fundamental role is played by a Sobolev vs. Hölder minima principle, already known for the degenerate case, which here we extend to the singular case with a simpler proof.

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• Existence of solutions for nonlinear equations with mixed local and nonlocal operators

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