Viable periodic solutions in state-dependent impulsive problems

被引：5

作者：

Gabor, Grzegorz ^{[1
]}

机构：

[1] Nicholas Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

COLLECTANEA MATHEMATICA | 2015年 / 66卷 / 03期

关键词：

Periodic solution; Viable solution; Fixed point index; State-dependent impulsive problems; Impulse function; DIFFERENTIAL-INCLUSIONS; EXISTENCE;

D O I：

10.1007/s13348-015-0139-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Periodic solutions of state-dependent impulsive ODEs in a prescribed set of constraints are examined. The so-called impulsive index is introduced, as a topological tool, and its properties are studied. Some sufficient conditions for its homotopy property are discussed in detail. In a construction of the impulsive index the fixed point index on ANRs is applied to an induced discrete semidynamical system on a barrier where jumps occur. Several illustrative examples are added.

引用

页码：351 / 365

页数：15

共 20 条

[11]

Conley C., 1976, Lecture Notes in Math, V564, P61

[12] Homotopy index for multivalued flows on sleek sets [J].

Gabor, G .

SET-VALUED ANALYSIS, 2005, 13 (02) :125-149

[13] On existence of solutions to differential equations or inclusions remaining in a prescribed closed subset of a finite-dimensional space [J].

Gabor, G ;

Quincampoix, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 185 (02) :483-512

[14] The existence of viable trajectories in state-dependent impulsive systems [J].

Gabor, Grzegorz .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (9-10) :3828-3836

[15]

Gorniewicz L., 2006, Topological Fixed Point Theory of Set-valued Mappings, VSecond

[16]

Granas A., 2003, SPRINGER MG MATH

[17] Periodic solutions to impulsive differential inclusions with constraints [J].

Kryszewski, Wojciech ;

Plaskacz, Slawomir .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 65 (09) :1794-1804

[18]

Milman VD, 1960, Sib Math J, V1, P233

[19]

Nagumo M, 1942, Proc. Physico-Math. Soc. Japan. 3rd Series, V24, P551, DOI [DOI 10.11429/PPMSJ1919.24.0551, DOI 10.11429/PPMSJ1919.24.0_551]

[20]

Wazewski T., 1948, Ann. Soc. Polon. Math, V20, P279

← 1 2 →