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.