Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Homoclinic solutions for second order discrete pLaplacian systems | He and Chen Advances in Difference Equations 2011 2011 57 http content 2011 1 57 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Homoclinic solutions for second order discrete p-Laplacian systems Xiaofei He1 2 and Peng Chen2 3 Correspondence hxfcsu@sina. com department of Mathematics and Computer Science Jishou University Jishou Hunan 416000 P. R. China Full list of author information is available at the end of the article Springer Abstract Some new existence theorems for homoclinic solutions are obtained for a class of second-order discrete p-Laplacian systems by critical point theory a homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second-order difference systems. A completely new and effective way is provided for dealing with the existence of solutions for discrete p-Laplacian systems which is different from the previous study and generalize the results. 2010 Mathematics Subject Classification 34C37 58E05 70H05. Keywords homoclinic solutions discrete variational methods p-Laplacian systems 1. Introduction In this article we shall be concerned with the existence of homoclinic orbits for the second-order discrete Ji-Laplacian systems A p Au n - 1 VF n u n f n n e Z u e RN where p 1 ộp s s p-2s is the Laplacian operator Au n u n 1 - u n is the forward difference operator F z X RN R is a continuous function in the second variable and satisfies F n T u F n u for a given positive integer T. As usual N z and R denote the set of all natural numbers integers and real numbers respectively. For a b e z denote z a a a 1 . z a b a a 1 . b when a b. Differential equations occur widely in numerous settings and forms both in mathematics itself and in its application to statistics computing electrical circuit analysis biology and other fields so it is worthwhile to explore this topic. As is known to us the development of the study of periodic solution and .
