Second-order functional problems with a resonance of dimension one

Abstract

We obtain, using the coincidence degree theory, solvability conditions for all possible resonance scenarios Lu = u = f (t,u,u ) = Nu , with linear functional conditions B i u = 0 , i = 1,2 with dim ker L = 1 . Our work generalizes and improves the results of Zhao and Liang We also construct a meaningful example of a nonlinear functional problem for a pendulum equation which not only satisfies the assumptions of an existence theorem but also has a closed-form solution.