Free and constrained equilibrium states in a variational problem on a surface

Document Type : Research Paper

Author

Department of Physics and Mathematics, National Polytechnical Institute (I.P.N.), Campus Zacatecas (U.P.I.I.Z) P. C. 098160, Zacatecas, Mexico.

Abstract

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman's and Skrypnik's variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik's method, described in [P. Vyridis, {\it Bifurcation in a Variational Problem on a Surface with a Constraint}, Int. J. Nonlinear Anal. Appl. 2 (1) (2011), 1-10]. In local coordinates, equilibrium points satisfy an elliptic boundary value problem.

Keywords

Volume 6, Issue 1 - Serial Number 1
March 2015
Pages 119-134
  • Receive Date: 10 November 2013
  • Revise Date: 03 November 2014
  • Accept Date: 24 December 2014