A quadratic Bolza-type problem in a non-complete Riemannian manifold

Anna Maria Candela; J.L. Flores; M. Sánchez

doi:10.3934/proc.2003.2003.173

Article Contents

2003, Volume 2003: 173-181. Doi: 10.3934/proc.2003.2003.173 open access

This issue Previous Article Oscillation of mixed neutral differential equations with forcing term Next Article Blow-up estimates of positive solutions of a reaction-diffusion system

A quadratic Bolza-type problem in a non-complete Riemannian manifold

1.
Dipartimento Di Matematica, Universita' degli Studi di Bari "Aldo Moro", via E. Orabona 4, 70125 Bari
2.
Departamento de Álgebra, Geometría y Topología, Facultdad de Ciencias, Universidad de Granada, Avenida Fuentenueva s/n, 18071 Granada

Received: August 31, 2002

Revised: February 28, 2003

Published: March 2003

Abstract Related Papers Cited by

Abstract

Let the nonlinear equation $D_s(dotx) + \lambda \nabla_x V (x, s) = 0$ be defined in a non–complete Riemannian manifold $M$ and consider those ones of its solutions which join any couple of fixed points in $M$ in a fixed arrival time $T > 0$. If $V$ has a quadratic growth with respect to $x$ and if $M$ has a convex boundary, then a "best constant" $bar(\lambda)(T)>$ 0 exists such that if $0 \<= \lambda \< bar(\lambda)(T)$ the problem admits at least one solution while infinitely many ones exist if the topology of $M$ is not trivial.

Keywords:

Mathematics Subject Classification: 70H03, 58E05, 49J40.

Citation:

Article Metrics

HTML views() PDF downloads(56) Cited by(0)

A quadratic Bolza-type problem in a non-complete Riemannian manifold

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

A quadratic Bolza-type problem in a non-complete Riemannian manifold

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content