Existence results for a mixed boundary value problem

In the present paper, we obtain an existence result for a class of mixed boundary value problems for second-order differential equations. A critical point theorem is used, in order to prove the existence of a precise open interval of positive eigenvalues lambda, for which the considered problem admits at least one non-trivial classical solution u(lambda). It is proved that the norm of u(lambda) tends to zero as lambda -> 0.