International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 11-20
doi:10.1155/S0161171200001630

Nonlinear variational evolution inequalities in Hilbert spaces

Jin-Mun Jeong,1 Doo-Hoan Jeong,2 and Jong-Yeoul Park3

1Division of Mathematical Sciences, Pukyong National University, Pusan 608-737, Korea
2Dongeui Technical Junior College, Pusan 614-053, Korea
3Department of Mathematics, Pusan National University, Pusan 609-739, Korea

Received 31 July 1998

Copyright © 2000 Jin-Mun Jeong et al. 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

The regular problem for solutions of the nonlinear functional differential equations with a nonlinear hemicontinuous and coercive operator A and a nonlinear term f(.,.):x′(t)+Ax(t)+∂ϕ(x(t))∋f(t,x(t))+h(t) is studied. The existence, uniqueness, and a variation of solutions of the equation are given.