On Fast Homoclinic Solutions for Second-Order Damped Difference Equations

被引：3
|
作者：
Daouas, Adel [1 ]
Guefrej, Ameni [1 ]
机构：
[1] Sousse Univ, High Sch Sci & Technol, MaPSFA Lab, H Sousse 4011, Tunisia
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 04期
关键词：
Homoclinic solution; Fast solution; (PS) condition; Mountain pass theorem; Difference equations; EXISTENCE;
D O I：
10.1007/s40840-019-00858-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
By means of critical point theory, we study the existence and multiplicity of homoclinic solutions of the damped second-order difference equation 2u(n - 1) - c u(n - 1) - a(n)u(n) + f (n, u(n)) = 0, n. Z, where c > -1 is a constant, a : Z. (0,+8) and f : Z x R. R is continuous with respect to the second variable and satisfies some additional assumptions. The proofs of our results are based on variational methods in some weighted Hilbert space of sequences. Some recent results in the literature are extended even in the case of c = 0.
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页码：3125 / 3142
页数：18
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