Work

Resonance phenomena in the second differential order equations with nonlinear impulsive effects

Year: 2025

Type: article

Abstract: In this paper, we discuss the resonance phenomena in linear and weakly nonlinear impulsive differential equations. Using a topological approach, we obtain the Landesman–Lazer type necessary and sufficient conditions for the existence of periodic solutions and extend the Fredholm alternative for linear equations with impulses. Moreover, we show the coexistence of periodic and unbounded solutions of weakly nonlinear impulsive differential equations through the use of the successor map and a Lyapunov function.

Source: Electronic journal of qualitative theory of differential equations

DOI: 10.14232/ejqtde.2025.1.61

Authors: Fanfan Chen, Dingbian Qian, Nannan Xu

Institutions: Zhejiang Sci-Tech University, Soochow University, Suzhou University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Zhejiang Sci-Tech University, Natural Science Foundation of Zhejiang Province