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

Document Type : Research Paper


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


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.


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