Differential inclusion problems with convolution and discontinuous nonlinearities
type: Item
instance of: scholarly article
title: Differential inclusion problems with convolution and discontinuous nonlinearities
zbMATH Open document ID: 1464.35140
author: Yongjian Liu
author: Zhenhai Liu
author: Dumitru Motreanu
published in: Evolution Equations and Control Theory
publication date: 2021-01-13T00:00:00Z
review text: The authors study the quasilinear inclusion problem \[-\Delta_pu-\mu(x)\Delta_qu\in f(x,\rho*u,\nabla(\rho*u))+[\underline{g}(u),\overline{g}(u)] \ \text{in}\ \Omega,\quad u=0\text{ on }\ \partial\Omega,\] on a bounded domain \(\Omega\subset \mathbb{R}^N\), \(N\ge 2\), with \(p\)- and \(q\)-Laplacians \[\Delta_p:W_0^{1,p}(\Omega)\to W^{-1,p'}(\Omega), \ \Delta_q:W_0^{1,q}(\Omega)\to W^{-1,q'}(\Omega),\ 1<q<p<+\infty.\] The problem reduces to a quasilinear Dirichlet boundary value problem if \(g\) is continuous. The main results are existence and uniqueness theorems and the dependence of the solutions on the parameters of the inclusion.
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35J87
zbMATH DE Number: 7293862
zbMATH Keywords: weighted \((p, q)\)-Laplacian
zbMATH Keywords: differential inclusion
zbMATH Keywords: quasilinear Dirichlet boundary value problem
reviewed by: Igor Bock
MaRDI profile type: Publication
full work available at URL: eect.2020056
OpenAlex ID: W3026608470
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DOI: 10.3934/EECT.2020056
description: scientific article; zbMATH DE number 7293862