Multiplicity results for nonlinear mixed boundary value problem

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Multiplicity Results for a Perturbed Elliptic Neumann Problem

The existence of three solutions for elliptic Neumann problems with a perturbed nonlinear term depending on two real parameters is investigated. Our approach is based on variational methods

Infinitely Many Solutions for Perturbed Hemivariational Inequalities

Abstract We deal with a perturbed eigenvalue Dirichlet-type problem for an elliptic hemivariational inequality involving the -Laplacian. We show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of infinitely many solutions. The main tool in order to obtain our abstract results is a recent critical-point theorem for nonsmooth functionals

One-dimensional nonlinear boundary value problems with variable exponent

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Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions

In this paper, a nonlinear differential problem involving the $p$-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results

Infinitely many solutions for a class of quasilinear two-point boundary value systems

The existence of infinitely many solutions for a class of Dirichlet quasilinear elliptic systems is established. The approach is based on variational methods

Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional pp-Laplacian

The existence of three distinct weak solutions for a perturbed mixed boundary value problem involving the one-dimensional $p$-Laplacian operator is established under suitable assumptions on the nonlinear term. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces

Periodic solutions for second order Hamiltonian systems

In this paper we present some recent multiplicity results for a class of second order Hamiltonian systems. Exploiting the variational structure of the problem, it will be shown how the existence of multiple, even infinitely many, periodic solutions can be assured