Applied Mathematical Sciences, Vol. 7, 2013, no. 66, 3271 - 3280 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.33195 Existence of Equilibrium States of Hollow Hollomon Cylinders Submerged in a Fluid M. B. M. Elgindi Taxes A & M University in Qatar P.O. Box 23874, Doha, Qatar, mohamed.elgindi@qatar.tamu.edu D. Wei University of New Orleans, 2000 Lakeshore Drive New Orleans, LA 70148, USA dwei@uno.edu Copyright © 2013 M. B. M. Elgindi and D. Wei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper is concerned with the existence of equilibrium states of a thin-walled hollow elasto-plastic cylinders fully or partially submerged in a fluid. This problem serves as a model for many problems with engineering importance. Previous studies on the deformation of such a shell assumed that the material is linear elastic. This paper takes into consideration the nonlinear Hollomon materials that (are plastic) can deform plastically. The effect of gravity on pressure is also taken into account. Mathematics Subject Classification: 49G99, 73H05, 73K15 Keywords: Existence of equilibrium states, Hollomon power-law material, hollow plastic cylinders, nonlinear eigenvalue problem, nonlinear integro-differential equation, minimization of functional with constraints, Browder Theorem.