Existence of weak solutions of nonlinear functional differential equations with unbounded delay

Abstract

A phase space for first order partial functional differential equations is constructed. Weak solutions of initial problems are investigated. A theorem on the existence of solutions of initial problems is proved. The method of quasilinearhation of a nonlinear problem and functional integral inequalities are used.

Keywords:

• Initial problems
• unbounded delay
• phase spaces
• bicharacteristics
• functional integral equations

AMS:

• 35D05
• 35F25
• 35L60
• 35R10