arXiv subjects

Károly Szilák

Publications and source records attributed to Károly Szilák.

3 recordsLinked to original sources

arXiv2023

A Dirichlet inclusion problem on Finsler manifolds

In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator on a complete Finsler manifold. Depending on the positive $λ$ parameter of the inclusion, we establish non-existence, as well as existence and multiplicity results by applying non-smooth variational methods. The main difficulties are given by the problem's highly nonlinear nature due to the general Finslerian setting, as well as the nonsmooth context.

math.AP↗

arXiv2022

Elliptic differential inclusions on non-compact Riemannian manifolds

We investigate a large class of elliptic differential inclusions on non-compact complete Riemannian manifolds which involves the Laplace-Beltrami operator and a Hardy-type singular term. Depending on the behavior of the nonlinear term and on the curvature of the Riemannian manifold, we guarantee non-existence and existence/multiplicity of solutions for the studied differential inclusion. The proofs are based on nonsmooth variational analysis as well as isometric actions and fine eigenvalue properties on Riemannian manifolds. The results are also new in the smooth setting.

math.AP↗

arXiv2020

Differential inclusions involving oscillatory terms

Motivated by mechanical problems where external forces are non-smooth, we consider the differential inclusion problem \[ \begin{cases} -Δu(x)\in \partial F(u(x))+λ\partial G(u(x))\ \mbox{in}\ Ω\newline u\geq 0\ \mbox{in}\ Ω\newline u= 0\ \mbox{on}\ \partialΩ, \end{cases} \ \ \ \ \ \ \ \ \ \ \ \ {({\mathcal D}_λ)} \] where $Ω\subset {\mathbb R}^n$ is a bounded open domain, and $\partial F$ and $\partial G$ stand for the generalized gradients of the locally Lipschitz functions $F$ and $G$. In this paper we provide a quite complete picture on the number of solutions of $({\mathcal D}_λ)$ whenever $\partial F$ oscillates near the origin/infinity and $\partial G$ is a generic perturbation of order $p>0$ at the origin/infinity, respectively. Our results extend in several aspects those of Kristály and Moroşanu [J. Math. Pures Appl., 2010].

math.AP↗