Bifurcation of periodic solutions to nonlinear measure differential equations

TL;DR

This paper investigates the bifurcation phenomena of periodic solutions in nonlinear measure differential equations using advanced generalized differential equations and integral tools, extending previous research in the field.

Contribution

It introduces a new approach employing Kurzweil's generalized differential equations and integrals to analyze bifurcations in nonlinear measure differential equations.

Findings

Identification of bifurcation points for periodic solutions

Application of Kurzweil gauge type integrals in bifurcation analysis

Extension of previous bifurcation results to measure differential equations

Abstract

This paper is devoted to bifurcations of periodic solutions of nonlinear measure differential equations with a parameter. Main tools are nonlinear generalized differential equations (in the sense of Kurzweil) and the Kurzweil gauge type generalized integral. We continue the research started by the first author under the supervision of the second one.