Existence of solutions to a class of nonlinear second order two-point boundary value problems

Abstract

In this paper, the existence and multiplicity results of solutions are obtained for the second order two-point boundary value problem − u ″ ( t ) = f ( t , u ( t ) ) for all t ∈ [ 0 , 1 ] subject to u ( 0 ) = u ′ ( 1 ) = 0 , where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role.