Existence of solutions of a nonlinear differential equation

Abstract

A criterion is proved for the existence of at least one solution to the equation u + u = g ( u ) + h u + u = g(u) + h with u ( 0 ) = u ( π ) = 0 u(0) = u(\pi ) = 0 , where h ∈ L 2 [ 0 , π ] h \in {L_2}[0,\pi ] and g g is continuous monotone nonincreasing.