Existence and monotonicity property of minimizers of a nonconvexvariational problem with a second-order Lagrangian

Kaizhi Wang; Yong Li

doi:10.3934/dcds.2009.25.687

Article Contents

2009, Volume 25, Issue 2: 687-699. Doi: 10.3934/dcds.2009.25.687

This issue Previous Article Hölder forms and integrability of invariant distributions Next Article Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition

Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian

Kaizhi Wang^1, and
Yong Li^2,

1.
College of Mathematics, Jilin University, Changchun 130012
2.
Department of Mathematics, Jilin University, Changchun 130023

Received: July 31, 2008

Revised: December 31, 2008

Published: May 2009

Abstract Related Papers Cited by

Abstract

A variational problem

Minimize $\quad \int_a^bL(x,u(x),u'(x),u''(x))dx,\quad u\in\Omega$

with a second-order Lagrangian is considered. In absence of any smoothness or convexity condition on $L$, we present an existence theorem by means of the integro-extremal technique. We also discuss the monotonicity property of the minimizers. An application to the extended Fisher-Kolmogorov model is included.

Keywords:

Mathematics Subject Classification: Primary: 49K15, Secondary: 49J45.

Citation:

Article Metrics

HTML views() PDF downloads(72) Cited by(0)

Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content