Nonlinear variational evolution inequalities in Hilbert spaces

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.

Keywords

• Nonlinear variational evolution inequality
• maximal monotone operator
• subdifferential operator
• regularity.