Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or in...

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Bibliographic Details
Main Author: Coelho, Isabel (author)
Other Authors: Corsato, Chiara (author), Obersnel, Franco (author), Omari, Pierpaolo (author)
Format: article
Language:eng
Published: 2012
Subjects:
Quasilinear Ordinary Differential Equation
Minkowski-Curvature
Dirichlet Boundary Conditions
Positive Solution
Existence
Multiplicity
Critical Point Theory
Bifurcation Methods
Lower and Upper Solutions
Online Access:http://hdl.handle.net/10400.21/1824
Country:Portugal
Oai:oai:repositorio.ipl.pt:10400.21/1824
Description
Summary:We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

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