AN AVERAGING RESULT FOR PERIODIC SOLUTIONS OF CARATHEODORY DIFFERENTIAL EQUATIONS

Author(s)

Novaes, Douglas D.

• Document type: Journal article
• Source: Proceedings of the American Mathematical Society; v. 150, n. 7, p. 10-pg., 2022-07-01.

Abstract

This paper is concerned with the problem of existence of periodic solutions for perturbative Caratheodory differential equations. The main result provides sufficient conditions on the averaged equation that guarantee the existence of periodic solutions. Additional conditions are also provided to ensure the uniform convergence of a periodic solution to a constant function. The proof of the main theorem is mainly based on an abstract continuation result for operator equations. (AU)

• FAPESP's process: 21/10606-0 - On limit cycles in piecewise linear vector fields with algebraic discontinuity variety
• Grantee: Douglas Duarte Novaes
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/16430-8 - Global dynamics of nonsmooth differential equations
• Grantee: Douglas Duarte Novaes
• Support Opportunities: Regular Research Grants