Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68226120150301Free and constrained equilibrium states in a variational problem on a surface11913422310.22075/ijnaa.2015.223ENPanayotis VyridisDepartment of Physics and Mathematics, National Polytechnical Institute (I.P.N.), Campus Zacatecas (U.P.I.I.Z) P. C. 098160, Zacatecas, Mexico.Journal Article20131110We 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.https://ijnaa.semnan.ac.ir/article_223_a1f8208d0e720dfe30bb5073ee0b5d14.pdf