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September 10, 2025

Atypical bifurcation for periodic solutions of ϕ-Laplacian systems

Key Points

The study reveals atypical bifurcation of T-periodic solutions, illustrating new insights into ϕ-Laplacian systems.
Key results arise from applying topological degree theory, specifically related to bifurcation from λ = 0.
Applications to Liénard-type equations demonstrate the practical relevance of the obtained results.
The findings align with Prodi–Ambrosetti's framework, providing a deeper understanding of periodic solutions.

Abstract

Abstract In this paper, we study the T -periodic solutions of the parameter-dependent ϕ -Laplacian equation equation* ( (x') ) '=F (, t, x, x'). equation* Based on the topological degree theory, we present some atypical bifurcation results in the sense of Prodi–Ambrosetti, i. e. , bifurcation of T -periodic solutions from λ = 0. Finally, we propose some applications to Liénard-type equations. Dedicated to Professor Maria Patrizia Pera on the occasion of her 70th birthday

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