An application of Krasnoselskii fixed point theorem to the asymptotic behavior of solutions of difference equations in Banach spaces

被引：7

作者：

González, C ^{[1
]}

Jiménez-Melado, A ^{[1
]}

机构：

[1] Univ Malaga, Fac Ciencias, Dept Anal Matemat, E-29071 Malaga, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2000年 / 247卷 / 01期

关键词：

Krasnoselskii fixed point theorem; Banach space; difference equation; asymptotic behavior;

D O I：

10.1006/jmaa.2000.6877

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the first order difference equation Delta x(n) = (infinity)Sigma(i = 0) a(n)(i) f(x(n +) (1)) + infinity Sigma(i = 0) b(n)(i)g(x(n + i)) + y(n) and the second order difference equation Delta(q(n) Delta x(n)) + r(n) f(x(n)) + s(n)g (x) + z(n) = 0, where f is a Lipschitz mapping and g is a compact operator, both defined on a Banach space X. We give sufficient conditions so that there exist solutions which are asymptotically constant. These results generalize those given by A. Drozdowicz and J. Popenda (1987, Proc. Amer. Math. Sec. 99, 135-140), J. Popenda and E. Schmeidel (1994, Publ. Mat. 38, 3-9; 1997, Indian J. Pure Appl. Math. 28, 319-327), and E. Schmeidel (1997, Demonstratio Math. 30, 193-197: 1997; Comm. Appl. Nonlinear Anal. 4, 87-92). (C) 2000 Academic Press.

引用

页码：290 / 299

页数：10

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POPENDA, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 99 (01) :135-140

[4]

GONZALEZ C, IN PRESS P AM MATH S

[5]

Krasnoselskii M.A., 1955, Uspekhi Matematicheskikh Nauk, V10, P123, DOI DOI 10.1016/S0076-5392(08)61895-0

[6]

Popenda J, 1997, INDIAN J PURE AP MAT, V28, P319

[7]

POPENDA J, 1994, PUBL MAT, V38, P3

[8]

SCHMEIDEL E, 1997, COMM APPL NONLINEAR, V4, P87

[9]

Schmitz B, 1997, TEXT TRANS COMP PROC, V1, P193

[10]

ZEIDLER E., 1986, Nonlinear Functional Analysis and its Applications, VI

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