Existence and subharmonicity of solutions for nonsmooth $ p $-Laplacian systems

<abstract><p>In this paper we study nonlinear periodic systems driven by the vectorial $ p $-Laplacian with a nonsmooth locally Lipschitz potential function. Using variational methods based on nonsmooth critical point theory, some existence of periodic and subharmonic results are obtained, which improve and extend related works.</p></abstract>

Perturbation results involving the 1-Laplace operator

We consider perturbed eigenvalue problems of the 1-Laplace operator and verify the existence of a sequence of solutions. It is shown that the eigenvalues of the perturbed problem converge to the corresponding eigenvalue of the unperturbed problem as the perturbation becomes small. The results rely on nonsmooth critical point theory based on the weak slope.

Three Solutions for Fourth-Order Impulsive Differential Inclusions via Nonsmooth Critical Point Theory

An existence of at least three solutions for a fourth-order impulsive differential inclusion will be obtained by applying a nonsmooth version of a three-critical-point theorem. Our results generalize and improve some known results.

Existence and Multiplicity Results for A Fourth-Order Boundary Value Problem

In this paper we consider a class of a fourth-order boundary value problem. Using a variational method based on nonsmooth critical point theory, we prove the existence and multiplicity of solutions.