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

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.  2005 Elsevier Inc. All rights reserved