Equilibrium States Under Constraint in a Variational Problem on a Surface

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Authors

  • Panayotis Vyridis Department of Physics and Mathematics, National Polytechnic Institute (IPN), Campus Zacatecas(UPIIZ) P.C.098160, Zacatecas, Mexico Author
  • M.K. Christophe Ndjatchi Department of Physics and Mathematics, National Polytechnic Institute (IPN), Campus Zacatecas(UPIIZ) P.C.098160, Zacatecas, Mexico Author
  • Fernando García Flores Department of Physics and Mathematics, National Polytechnic Institute (IPN), Campus Zacatecas(UPIIZ) P.C.098160, Zacatecas, Mexico Author
  • Julio César Flores Urbina Department of Physics and Mathematics, National Polytechnic Institute (IPN), Campus Zacatecas(UPIIZ) P.C.098160, Zacatecas, Mexico Author

DOI:

https://doi.org/10.5890/DNC.2016.03.004

Abstract

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface under a constraint of geometrical character. We use an improved method, based in Skrypnik’s variational theories [10]. In local coordinates, equilibrium points satisfy an elliptic boundary value problem. This model can be described as the deformation of the elastic medium and membranes.

References

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[2] Vyridis, P. (2002), Variational Problem on Equilibrium of an Elastic Medium, Located in an Elastic Shell, J. Math. Sci. (N.Y.) 112(1), 3992.

[3] Vyridis, P. (2011), Bifurcation in a Variational problem on a surface with a constraint, Int. J. Nonlinear Anal. Appl. 2 (1), 1–10.

[4] Vyridis, P.(2014), Bifurcation in a Variational problem on a surface with a distance constraint, J. of Nonlinear Sci. Appl. 7, 160–167.

[5] Giusti, E. (1984), Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, Vol. 80, Birkhäuser, Boston-Basel-Stuttgart.

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[7] Gilbarg, D. and Trüdinger, N.S. (1977) Elliptic Partial Differential Equations of Second Order, Springer-Verlag.

[8] Osmolovskii, V.G. (1997), Linear and nonlinear pertubations of operator div, Translations of Mathematical Monographs, Vol. 160.

[9] Osmolovskii, V.G. (2000), The Variational Problem on Phase Transitions in Mechanics of Continuum Media , St. Petersburg University Publications.

[10] Skrypnik, I.V. (1973), Nonlinear Partial Differential Equations of Higher Order, Kiev.

[11] Skrypnik, I.V.(1976), Solvability and properties of solutions to nonlinear elliptic equations, Recent Problems in Mathematics, VINITI, 9, 131–242.

[12] Dubrovin, B.A., Fomenko, A.T., and Novikov, S.P. (1990), Modern Geometry - Methods and Applications, Part I, Spinger - Verlag New York Inc.

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PublishedMarch 2016

Usage tracking begins September 1, 2026.

History Published

Issue

Vol. 5 No. 1 (2016): Regular Issue

Section

Research Articles

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Unless an article landing page states a Creative Commons or other article-specific license, the article is published by L&H Scientific Publishing, LLC and all rights are reserved. The article-level license and copyright notice govern access and reuse.

How to Cite

Vyridis, P., Ndjatchi, M. C., Flores, F. G., & Urbina, J. C. F. (2026). Equilibrium States Under Constraint in a Variational Problem on a Surface. Discontinuity, Nonlinearity, and Complexity, 5(1), 25-32. https://doi.org/10.5890/DNC.2016.03.004

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