Hybrid Nehari-Krasnosel’skiĭ type results and applications

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Abstract

In this paper, we present a new hybrid fixed point theorem for systems. Our approach yields a solution with nontrivial components lying on a Nehari-type manifold, whose second component is localized in an annular conical set. We establish two main results. In the first, the localization of the second component is obtained via the fixed point index and lies in a set determined by a norm and a seminorm, while the second result uses a geometric approach in the spirit of Krasnosel’skiĭ, ensuring that the norm of the second component belongs to a prescribed interval. For each of these results, we provide an application.

Authors

Laura M Fernández–Pardo
CITMAga, Santiago de Compostela, 15782, Spain
Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vida, Santiago de Compostela, 15782, Spain

Jorge Rodríguez–López
CITMAga, Santiago de Compostela, 15782, Spain
Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vida, Santiago de Compostela, 15782, Spain

Andrei Stan
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Upper and lower solution, Harnack inequality, fixed point

Paper coordinates

Fernández–Pardo, L. M., Rodríguez–López, J., Stan, A. Hybrid Nehari-Krasnosel’skiĭ type results and applications. J. Differ. Equ. 476, 114481 (2026). https://doi.org/10.1016/j.jde.2026.114481

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https://www.sciencedirect.com/science/article/pii/S0022039626003888

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https://doi.org/10.1007/s00025-026-02631-6

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