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arXiv · 2603.23077

A unified treatment of degenerate nonlocal elliptic problems

L. Gasinski·H. Ramos Quoirin·J. Santos Junior·K. Silva
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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.

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L. Gasinski, H. Ramos Quoirin, J. Santos Junior, K. Silva. 2026-03-24. A unified treatment of degenerate nonlocal elliptic problems. https://arxiv.org/abs/2603.23077

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