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

2025/11/27 by Antonio Iannizzotto, Iannizzotto, Antonio
Mathematics · #35A15 #35R11 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2511.22620

openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/30

Abstract

We study an elliptic equation, with homogeneous Dirichlet boundary conditions, driven by a mixed type operator (the sum of the Laplacian and the fractional Laplacian), involving a parametric reaction and an undetermined source term. Applying a recent abstract critical point theorem of Ricceri, we prove existence of a solution for a convenient source and small enough parameters.

Citations

• On a doubly sublinear fractional p-Laplacian equation
• A Brezis-Oswald approach for mixed local and nonlocal operators
• On the logistic equation for the fractional p-Laplacian
• (Non)local logistic equations with Neumann conditions
• Mixed local and nonlocal elliptic operators: regularity and maximum\n principles
• Hitchhiker's guide to the fractional Sobolev spaces

Related

• Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators
• Global and nonglobal solutions for a mixed local-nonlocal heat equation
• Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space
• Semilinear Equations Including the Mixed Operator
• Positive solutions for a class of nonlocal problems with possibly singular nonlinearity