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.
Vyridis, P. (2015). Free and constrained equilibrium states in a variational problem on a surface. International Journal of Nonlinear Analysis and Applications, 6(1), 119–134. https://doi.org/10.22075/ijnaa.2015.223
MLA
Vyridis, P. "Free and constrained equilibrium states in a variational problem on a surface", International Journal of Nonlinear Analysis and Applications, 6, 1, 2015, 119–134. doi: 10.22075/ijnaa.2015.223
HARVARD
Vyridis, P. (2015). 'Free and constrained equilibrium states in a variational problem on a surface', International Journal of Nonlinear Analysis and Applications, 6(1), pp. 119–134. doi: 10.22075/ijnaa.2015.223
CHICAGO
Vyridis, P., "Free and constrained equilibrium states in a variational problem on a surface." International Journal of Nonlinear Analysis and Applications, 6 1 (2015): 119–134, doi: 10.22075/ijnaa.2015.223
VANCOUVER
Vyridis P. Free and constrained equilibrium states in a variational problem on a surface. IJNAA. 2015;6(1):119–134. doi: 10.22075/ijnaa.2015.223
International Journal of Nonlinear Analysis and Applications