Existence results for a mixed boundary value problem

Abstract

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 $\lambda \rightarrow 0$.

Keywords

• mixed boundary value problems
• existence results
• critical points theory