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Behzad Djafari Rouhani Hadi Khatibzadeh 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e147
By using previous results of Djafari Rouhani [B. Djafari Rouhani, Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. Thesis, Yale university, 1981, part I, pp. 1-76; B. Djafari Rouhani, Asymptotic behaviour of quasi-autonomous dissipative systems in Hilbert spaces, J. Math. Anal. Appl. 147 (1990) 465-476; B. Djafari Rouhani, Asymptotic behaviour of almost nonexpansive sequences in a Hilbert space, J. Math. Anal. Appl. 151 (1990) 226-235] for dissipative systems, we study the asymptotic behavior of solutions to the following system of second-order nonhomogeneous evolution equations:
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Consider the retarded difference equationx
n
−x
n−1
=F(−f(x
n
)+g(x
n−k
)), wherek is a positive integer,F,f,g:R→R are continuous,F andf are increasing onR, anduF(u)>0 for allu≠0. We show that whenf(y)≥g(y) (resp. f(y)≤g(y)) fory∈R, every solution of (*) tends to either a constant or −∞ (resp. ∞) asn→∞. Furthermore, iff(y)≡g(y) fory∈R, then every solution of (*) tends to a constant asn→∞.
Project supported by NNSF (19601016) of China and NSF (97-37-42) of Hunan 相似文献
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N.C. Apreutesei 《Journal of Mathematical Analysis and Applications》2003,288(2):833-851
Of concern is the existence and uniqueness of the solution to a class of abstract second-order difference equations. They are the discrete version of some evolution equations which are intensely studied. Some asymptotic behavior results are established. The periodic solutions are also investigated. We use the theory of the maximal monotone operators in Hilbert spaces. An application to a partial differential equation is given. 相似文献
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蒋建初 《纯粹数学与应用数学》2002,18(1):26-31
考虑非线性差分方程△(Pn-1△(yn-1)^σ) qnf(yn)=0,n=1,2,3…其中linn→∞∑s=1^nqs存在且为有限给出了方程(E)具有渐近于非零常数解的必要(充分)条件。 相似文献
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Asymptotic behavior of solutions to a class of nonlinear wave equations of sixth order with damping 下载免费PDF全文
We investigate the initial value problem for a class of nonlinear wave equations of sixth order with damping. The decay structure of this equation is of the regularity‐loss type, which causes difficulty in high‐frequency region. By using the Fourier splitting frequency technique and energy method in Fourier space, we establish asymptotic profiles of solutions to the linear equation that is given by the convolution of the fundamental solutions of heat and free wave equation. Moreover, the asymptotic profile of solutions shows the decay estimate of solutions to the corresponding linear equation obtained in this paper that is optimal under some conditions. Finally, global existence and optimal decay estimate of solutions to this equation are also established. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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In this paper, using critical point theory, some sufficient conditions are obtained for the existence of periodic solutions of a class of second order difference equation. 相似文献
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We establish a precise estimate of the ultimate bound of solutions to some second order evolution equations with possibly unbounded linear damping and bounded forcing term. 相似文献