An intermediate local–nonlocal logistic elliptic equation with indefinite weight

Abstract

In this work, we study the logistic equation with an indefinite weight and a nonlocal diffusion operator. We first apply local and global bifurcation results to establish the existence of positive solutions. Next, we use approximation methods to obtain solutions under weaker regularity assumptions on the terms of the equation. Finally, we consider a particular case and carry out a sharp analysis of the solutions through bifurcation and fixed-point techniques, highlighting the complexity of their structure.