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
Andra Malina
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Andrei Stan
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Bazykin model, Localized solution, Periodic solution
Paper coordinates
Malina, A., Stan, A. Componentwise localization of positive periodic solutions for a general Bazykin-type system. Nonlinear Anal. Real World Appl. 94, 104701 (2027). https://doi.org/10.1016/j.nonrwa.2026.104701
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