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Topological Methods in Nonlinear Analysis

On the study of variational inequality of generalized Marguerre-von Kármán's type via Leray-Schauder degree
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On the study of variational inequality of generalized Marguerre-von Kármán's type via Leray-Schauder degree

Authors

  • Abderrezak Ghezal https://orcid.org/0000-0002-8502-7047

Keywords

Topological degree, variational inequalities, unilateral problem, Marguerre-von Kármán shallow shells

Abstract

The objective of this work is to study the existence theory for a class of variational inequalities of generalized Marguerr-von Kármán's type, which model unilateral problem for the buckling of generalized Marguerre-von Kármán shallow shells. More specifically, we reduce this problem to a variational inequality with cubic operator. Then, we prove the existence of solutions to this problem by using the Leray-Schauder degree.

References

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Melvyn S. Berger and Paul C. Fife, Von Kármán’s equations and the buckling of a thin elastic plate, II. Plate with general edge conditions, Comm. Pure Appl. Math. 21 (1968), 227–241.

D.A. Chacha, A. Ghezal and A. Bensayah, Existence result for a dynamical equations of generalized Marguerre–von Kármán shallow shells, J. Elasticity 111 (2013), 265–283.

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J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Éc. Norm. Supér. 51 (1934), 45–78.

K. Marguerre, Zur Theorie der gekrummten Platte grosser Formanderung, Proceedings, Fifth International Congress for Applied Mechanics, 1938, pp. 93–101.

J. Mawhin, Leray–Schauder degree: A half a century of extensions and applications, Topol. Methods Nonlinear Anal. 14, (1999), 195–228.

D. O’Regan, J. Cho and Yu-Qing Chen, Topological Degree Theory and Applications, Chapman and Hall/CRC, 2006.

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Published

2020-03-04

How to Cite

1.
GHEZAL, Abderrezak. On the study of variational inequality of generalized Marguerre-von Kármán’s type via Leray-Schauder degree. Topological Methods in Nonlinear Analysis. Online. 4 March 2020. Vol. 55, no. 1, pp. 369 - 383. [Accessed 2 July 2025].
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