Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation-Reference-Cited by-同舟云学术

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

Published:2012-08-01 Issue:3 Volume:12 Page:621-638
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Coelho Isabel¹²,Corsato Chiara³,Obersnel Franco³,Omari Pierpaolo³

Affiliation:

1. Área Departamental de Matemática Instituto Superior de Engenharia de Lisboa Rua Conselheiro Emídio Navarro 1, 1950-062 Lisboa, Portugal

2. D´epartement de Mathématique, Université Libre de Bruxelles, CP 214 Boulevard du Triomphe, 1050 Bruxelles, Belgium

3. Dipartimento di Matematica e Geoscienze Università degli Studi di Trieste Via A. Valerio 12/1, 34127 Trieste, Italy

Abstract

Abstract We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation

. 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2012-0310/pdf

Reference7 articles.

1. surfaces in Lorentzian manifolds;Gerhardt;Math Phys,1983

2. On some linear and nonlinear eigenvalue problems with an indefinite weight func - tion Differential;Hess;Partial Equations,1980

3. Spacelike hypersurfaces with prescribed boundary values and mean curvature;Bartnik;Math Phys,1982

4. Existence and multiplicity results for some nonlinear problems with singular φ;Bereanu;Differential Equations,2007

5. Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential Differential;Omari;Partial Equations,1996

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