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

摘要

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 E [0, 11 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. (c) 2005 Elsevier Inc. All rights reserved.