Classical and non-classical solutions of a prescribed curvature equation

We discuss existence and multiplicity of positive solutions of the one-dimensional prescribed curvature problem − ( u ′ / 1 + u ′ 2 ) ′ = λ f ( t , u ) , u ( 0 ) = 0 , u ( 1 ) = 0 , depending on the behaviour at the origin and at infinity of the potential ∫ 0 u f ( t , s ) d s . Besides solutions in...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2007-12, Vol.243 (2), p.208-237
Main Authors: Bonheure, Denis, Habets, Patrick, Obersnel, Franco, Omari, Pierpaolo
Format: Article
Language:English
Subjects:
Existence
Multiplicity
Positive solution
Prescribed curvature equation
Regularization
Two-point boundary value problem
Variational method
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss existence and multiplicity of positive solutions of the one-dimensional prescribed curvature problem − ( u ′ / 1 + u ′ 2 ) ′ = λ f ( t , u ) , u ( 0 ) = 0 , u ( 1 ) = 0 , depending on the behaviour at the origin and at infinity of the potential ∫ 0 u f ( t , s ) d s . Besides solutions in W 2 , 1 ( 0 , 1 ) , we also consider solutions in W loc 2 , 1 ( 0 , 1 ) which are possibly discontinuous at the endpoints of [ 0 , 1 ] . Our approach is essentially variational and is based on a regularization of the action functional associated with the curvature problem.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2007.05.031