Beatrice Di Bella

Non-trivial solutions for nonlinear fourth-order elastic beam equations

Abstract The existence of at least one non-trivial solution to a boundary value problem for fourth-order elastic beam equations, under a non-standard growth condition of the nonlinear term, is established. Our approach is based on a local minimum theorem for differentiable functionals.

A fourth-order boundary value problem for a Sturm–Liouville type equation

Abstract An existence result of multiple solutions for a fourth-order Sturm–Liouville boundary value problem with variable parameters is established. As a consequence, three solutions for a boundary value problem with a fourth-order equation in a complete form are obtained. Our approach is based on variational methods.

Infinitely many solutions for a boundary value problem with impulsive effects

In this paper we are interested in multiplicity results for a nonlinear Dirichlet boundary value problem subject to perturbations of impulsive terms. The study of the problem is based on the variational methods and critical point theory. Infinitely many solutions follow from a recent variational result.MSC:34B37, 34B15.

Comment: On a paper by J.M. Soriano

In this comment we want to show that Theorem 1 can be immediately derived from a classical theorem on the existence of zeros.