Existence of solutions for nonlinear equations with mixed local and nonlocal operators
Analysis of PDEs
2025-12-02 v2
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.
Keywords
Cite
@article{arxiv.2511.22620,
title = {Existence of solutions for nonlinear equations with mixed local and nonlocal operators},
author = {Antonio Iannizzotto},
journal= {arXiv preprint arXiv:2511.22620},
year = {2025}
}
Comments
7 pages