%0 Journal Article
%T Free and constrained equilibrium states in a variational problem on a surface
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Vyridis, Panayotis
%D 2015
%\ 03/01/2015
%V 6
%N 1
%P 119-134
%! Free and constrained equilibrium states in a variational problem on a surface
%K Calculus of Variations
%K Critical points for the Energy Functional
%K Boundary Value Problem for an Elliptic PDE
%K Surface
%K Curvature
%R 10.22075/ijnaa.2015.223
%X 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.
%U https://ijnaa.semnan.ac.ir/article_223_a1f8208d0e720dfe30bb5073ee0b5d14.pdf