tailieunhanh - báo cáo hóa học:" Research Article On Homoclinic Solutions of a Semilinear p-Laplacian Difference Equation with Periodic Coefficients"

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 On Homoclinic Solutions of a Semilinear p-Laplacian Difference Equation with Periodic Coefficients | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 195376 17 pages doi 2010 195376 Research Article On Homoclinic Solutions of a Semilinear p-Laplacian Difference Equation with Periodic Coefficients Alberto Cabada 1 Chengyue Li 2 and Stepan Tersian3 1 Departamento de Andlise Matemdtica Facultade de Matemdticas Universidade de Santiago de Compostela 15782 Santiago de Compostela Spain 2 Department of Mathematics Minzu University of China Beijing 100081 China 3 Department of Mathematical Analysis University ofRousse 7017 Rousse Bulgaria Correspondence should be addressed to Alberto Cabada Received 5 July 2010 Accepted 27 October 2010 Academic Editor Jianshe Yu Copyright 2010 Alberto Cabada et al. 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. We study the existence of homoclinic solutions for semilinear p-Laplacian difference equations with periodic coefficients. The proof of the main result is based on Brezis-Nirenberg s Mountain Pass Theorem. Several examples and remarks are given. 1. Introduction This paper is concerned with the study of the existence of homoclinic solutions for the p-Laplacian difference equation Apu k - 1 - V k u k u k q-2 Af k u ky 0 u t 0 t TO where u k k el is a sequence or real numbers A is the difference operator Au k u k 1 - u k Apu k - 1 Au k Au k p-2 - Au k - 1 Au k - 1 p-2 2 Advances in Difference Equations is referred to as the p-Laplacian difference operator and functions V k and f k x are T-periodic in k and satisfy suitable conditions. In the theory of differential equations a trajectory x t which is asymptotic to a constant as t TO is called doubly asymptotic or homoclinic orbit. The notion of homoclinic orbit is introduced by Poincare 1 for continuous Hamiltonian systems. Recently there is a large

TÀI LIỆU LIÊN QUAN