On the generalization of second order nonlinear anti-periodic boundary value problems

Abstract

This paper studies the existence of solutions for a second order boundary value problem of the type $$\left\{\begin{array}{cc} u''=f(t,u),\\ \ u(0)=\mu u(T), ~~u'(0)=\mu u'(T). \end{array} \right.$$ The main tool of study is Leray-Schauder degree theory.