Gradient and Parameter Dependent Dirichlet (p(x),q(x))-Laplace Type Problem

We analyze a Dirichlet (p(x),μq(x))-Laplace problem. For a gradient dependent nonlinearity of Carathéodory type, we discuss the existence, uniqueness and asymptotic behavior of weak solutions, as the parameter μ varies on the non-negative real axis. The results are obtained by applying the propertie...

Full description

Saved in:

Bibliographic Details
Published in:	Mathematics (Basel) Vol. 10; no. 8; p. 1336
Main Authors:	Albalawi, Kholoud Saad, Alharthi, Nadiyah Hussain, Vetro, Francesca
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-04-2022
Subjects:	Asymptotic properties Banach spaces Dirichlet problem gradient dependent term Inequality Lebesgue and Sobolev spaces with variable exponents Mathematics Nemitsky map Parameters parametric problems pseudomonotone operator
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We analyze a Dirichlet (p(x),μq(x))-Laplace problem. For a gradient dependent nonlinearity of Carathéodory type, we discuss the existence, uniqueness and asymptotic behavior of weak solutions, as the parameter μ varies on the non-negative real axis. The results are obtained by applying the properties of pseudomonotone operators, jointly with certain a priori estimates.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math10081336