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Type: Artigo de periódico
Title: Quasilinear equations with dependence on the gradient
Author: De Figueiredo, DG
Sanchez, J
Ubillac, P
Abstract: We discuss the existence of positive solutions of the problem - (q(t)phi(u'(t)))' = f (t, u(t), u'(t)) for t is an element of (0, 1) and u(0) = u(1) = 0. where the nonlinearity f satisfies a superlinearity condition at 0 and a local superlinearity condition at +infinity. This general quasilinear differential operator involves a weight q and a main differentiable part phi which is not necessarily a power. Due to the superlinearity off and its dependence on the derivative, a condition of the Bernstein-Nagumo type is assumed, also involving the differential operator. Our main result is the proof of a priori bounds for the eventual solutions. The presence of the derivative in the right-hand side of the equation requires a priori bounds not only on the solutions themselves, but also on their derivatives, which brings additional difficulties. As an application, we consider a quasilinear Dirichlet problem in an annulus {-div (A(vertical bar del u vertical bar)del u) = f(vertical bar x vertical bar, u, vertical bar del u vertical bar) in r(1) < vertical bar x vertical bar < r(2), u(x) = 0 on vertical bar x vertical bar = R(1) and vertical bar x vertical bar = R(2). (C) 2009 Elsevier Ltd. All rights reserved.
Subject: Positive radial solutions
Fixed points
Annular domains
Bernstein-Nagumo condition
Country: Inglaterra
Editor: Pergamon-elsevier Science Ltd
Rights: fechado
Identifier DOI: 10.1016/
Date Issue: 2009
Appears in Collections:Unicamp - Artigos e Outros Documentos

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