Asymptotic behavior of solutions of nonlinear functional differential equations

Abstract

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt+Au(t)+G(u)(t)?f(t), where A is a maximal monotone operator in a Hilbert space H, f?L1(0,8:H) and G:C([0,8):D(A)¯)?L1(0,8:H) is a given mapping.

Keywords

• almost nonexpansive curve
• maximal monotone operator
• generalized solution
• asymptotic behavior.