A unified treatment of degenerate nonlocal elliptic problems
Analysis of PDEs
2026-03-25 v1
Abstract
We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having sublinear or asymptotically linear growth. By combining the study of a suitable auxiliary problem and fixed-point techniques with careful parameter analysis, we establish existence, non-existence, and multiplicity results for positive solutions. Our method reveals sharp parameter thresholds and provides a comprehensive description of the solution set. Finally, for powerlike nonlinearities (including superlinear and singular ones) we provide a more direct approach, based on homogeneity.
Keywords
Cite
@article{arxiv.2603.23077,
title = {A unified treatment of degenerate nonlocal elliptic problems},
author = {L. Gasinski and H. Ramos Quoirin and J. Santos Junior and K. Silva},
journal= {arXiv preprint arXiv:2603.23077},
year = {2026}
}