On a class of nonlinear elliptic equations with lower order terms.
type: Item
instance of: scholarly article
title: On a class of nonlinear elliptic equations with lower order terms.
zbMATH Open document ID: 1424.35164
author: A. Mercaldo
author: Angelo Alvino
author: Roberta Volpicelli
author: Maria Francesca Betta
published in: Differential and Integral Equations
publication date: 2019-03-15T00:00:00Z
review text: The authors prove existence result for weak solutions of Dirichlet problem associated to a \(p\)-Laplace operator applying Schauder's fixed point theorem. Some difficulties occur when one tries to apply it directly, due to the presence of the first order term. The authors begin by considering a sequence of approximated problems obtained by truncations of the gradient term and, then, by using Schauder's fixed point theorem, under smallness assumptions on the datum and coefficient, prove that the approximated problems have weak solutions satisfying some a priori estimates. A standard procedure of passage to the limit allows to get the existence result for the Dirichlet problem.
reviewed by: Maria Alessandra Ragusa
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 7036981
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: existence
zbMATH Keywords: Dirichlet problem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7036981