Problems at Resonance for First and Second Order Differential Equations Via Lyapunov-Like Functions
Abstract
**Please note that the full text is embargoed** ABSTRACT: Recently [7,8,10] an attempt is made successfully to combine the two basic techniques namely, Lyapunov-Schmidt method and the method of upper and lower solutions, to investigate the existence of periodic solutions of differential equations. When we wish to extend such results for systems of differential equations there are two possibilities to follow. One is
to generalize the method of upper and lower solutions using a suitable cone, and the other is to utilize the concept of tyapunov-like functions and the theory of differential inequalities. In the paper, we shall discuss the existence
of problems at resonance for first and second order differential systems by the second approach developing necessary theory of differential inequalities for problems at resonance.