Existence and uniqueness on periodic solutions of fourth-order nonlinear differential equations

Abstract

In this paper, we study the problem of periodic solutions for fourth-order nonlinear differential equations. Under proper conditions, we employ a novel proof to establish some criteria to ensure the existence and uniqueness of $T$-periodic solutions. Moreover, we give two examples to illustrate the effectiveness of our main results.

Keywords

• fourth-order nonlinear differential equation
• periodic solution
• mawhin's continuation theorem