A multiplicity theorem for a class of nonlocal elliptic equations involving even nonlinearities

Biagio Ricceri

A multiplicity theorem for a class of nonlocal elliptic equations involving even nonlinearities

Analysis of PDEs 2026-07-20 v1

Authors: Biagio Ricceri

Abstract

In this paper, on a bounded domain $\Omega\subset {\bf R}^n$ , we consider a nonlocal problem of the type $\cases{-\Delta u=Q(u,\lambda)f(u) & in $\Omega$ \cr & \cr u=0 & on $\partial\Omega$\cr}$ where $Q:H^1_0(\Omega)\times {\bf R}\to {\bf R}$ , proving, under suitable assumptions, the existence of at least three weak solutions for each $\lambda$ running in a suitable interval.

Keywords

nonlocal elliptic equations even nonlinearities multiplicity theorem weak solutions bounded domain

Cite

@article{arxiv.2607.17969,
  title  = {A multiplicity theorem for a class of nonlocal elliptic equations involving even nonlinearities},
  author = {Biagio Ricceri},
  journal= {arXiv preprint arXiv:2607.17969},
  year   = {2026}
}