Free and constrained equilibrium states in a variational problem on a surface | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 16، دوره 6، شماره 1، 2015، صفحه 119-134 اصل مقاله (389.49 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2015.223 | ||
| نویسنده | ||
| Panayotis Vyridis | ||
| Department of Physics and Mathematics, National Polytechnical Institute (I.P.N.), Campus Zacatecas (U.P.I.I.Z) P. C. 098160, Zacatecas, Mexico. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Calculus of Variations؛ Critical points for the Energy Functional؛ Boundary Value Problem for an Elliptic PDE؛ Surface؛ Curvature | ||
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