Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 60239, 9 pages
doi:10.1155/2007/60239
Research Article

Slowly Oscillating Solutions for Differential Equations with Strictly Monotone Operator

Chuanyi Zhang and Yali Guo

 Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 2 August 2006; Accepted 28 February 2007

Recommended by Ondrej Dosly

Abstract

The authors discuss necessary and sufficient conditions for the existence and uniqueness of slowly oscillating solutions for the differential equation u'+F(u)=h(t) with strictly monotone operator. Particularly, the authors give necessary and sufficient conditions for the existence and uniqueness of slowly oscillating solutions for the differential equation u'+∇Φ(u)=h(t), where ∇Φ denotes the gradient of the convex function Φ on ℝN.