tailieunhanh - Báo cáo hóa học: " Research Article Slowly Oscillating Solutions for Differential Equations with Strictly Monotone Operator

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Slowly Oscillating Solutions for Differential Equations with Strictly Monotone Operator | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 60239 9 pages doi 2007 60239 Research Article Slowly Oscillating Solutions for Differential Equations with Strictly Monotone Operator Chuanyi Zhang and Yali Guo Received 2 August 2006 Accepted 28 February 2007 Recommended by Ondrej Dosly 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 VO u h t where VO denotes the gradient of the convex function O on RN. Copyright 2007 C. Zhang and Y. Guo. 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. 1. Introduction In this paper we will consider the following differential equation u F u h t where the maps h R RN and F RN RN are continuous. A special class of the dissipative equation is the case where the field F is derived from a convex potential O u vO u h t . For the dissipative equation Biroli 1 Dafermos 2 Haraux 3 Huang 4 and Ishii 5 have given important contributions to the question of almost periodic solutions which are valid even for the abstract evolution equations. In 6 Philippe Cieutat gives necessary and sufficient conditions for the existence and uniqueness of the bounded resp. almost periodic solution of when the forcing term h t is bounded resp. almost periodic . In the scalar case N 1 Slyusarchuk established similar results in 7 . But the conditions which are established in 6 for do not hold for even in 2 Journal of Inequalities and Applications the linear case. So in 6 Cieutat also gives a sufficient condition then a .