MULTIPLE POSITIVE SOLUTIONS OF A ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE PROBLEM-Reference-Cited by-同舟云学术

MULTIPLE POSITIVE SOLUTIONS OF A ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE PROBLEM

Published:2007-10 Issue:05 Volume:09 Page:701-730
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

HABETS PATRICK¹,OMARI PIERPAOLO²

Affiliation:

1. Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium

2. Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy

Abstract

We discuss existence, non-existence and multiplicity of positive solutions of the Dirichlet problem for the one-dimensional prescribed curvature equation [Formula: see text] in connection with the changes of concavity of the function f. The proofs are based on an upper and lower solution method, we specifically develop for this problem, combined with a careful analysis of the time-map associated with some related autonomous equations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199707002617

Reference23 articles.

1. Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems

2. Ground States for the Prescribed Mean Curvature Equation: The Supercritical Case

3. On a Modified Capillary Equation

4. A Prescribed Mean Curvature Problem on Domains without Radial Symmetry

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