Positive solutions for a class of implicit and discontinuous second order functional differential equations with singularities.
type: Item
instance of: scholarly article
title: Positive solutions for a class of implicit and discontinuous second order functional differential equations with singularities.
zbMATH Open document ID: 1035.34068
DOI: 10.1016/S0096-3003(02)00087-5
author: Alberto Cabada
author: J. Ángel Cid
author: Rodrigo L. Pouso
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: The authors deal with existence and approximation of a positive solution for the following implicit second-order problem \[ Lu(x)=q(x,u,Lu)\quad \text{a.e. }x\in [0,\alpha], \qquad u(0)=0,~k(u(0),u)u'(0)=0, \] with \[ Lu(x):=\frac{1}{u(x)}\left[(k(u(x),u)u'(x))'-f(x,u(x),u)u'(x)\right]-g(x,u(x),u). \] This problem shows singularities, discontinuous, functional dependence and arises in real phenomena in connection with diffusion.
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 1977931
zbMATH Keywords: discontinuous differential equations
zbMATH Keywords: functional-differential equations
zbMATH Keywords: positive solutions
reviewed by: Leonid Berezansky
MaRDI profile type: Publication
cites work: Q5312819
cites work: Existence results and approximation methods for functional ordinary differential equations with singular diffusion-type differential operators
cites work: Extremality results for discontinuous explicit and implicit diffusion problems
cites work: Approximate solutions to a new class of nonlinear diffusion problems
cites work: Q4492741
cites work: Q4303531
cites work: Existence, uniqueness, and approximation of solutions to some nonlinear diffusion problems
full work available at URL: s0096-3003(02)00087-5
OpenAlex ID: W2073698336
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description: scientific article; zbMATH DE number 1977931