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International Journal of Nonlinear Analysis and Applications
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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. doi: 10.22075/ijnaa.2015.223
Panayotis Vyridis. "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
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
Vyridis, P. Free and constrained equilibrium states in a variational problem on a surface. International Journal of Nonlinear Analysis and Applications, 2015; 6(1): 119-134. doi: 10.22075/ijnaa.2015.223

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

Article 16, Volume 6, Issue 1, Winter and Spring 2015, Page 119-134  XML PDF (389 K)
Document Type: Research Paper
DOI: 10.22075/ijnaa.2015.223
Author
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.
Abstract
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.
Keywords
Calculus of Variations; Critical points for the Energy Functional; Boundary Value Problem for an Elliptic PDE; Surface; Curvature
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