On the Dirichlet problem in billiard spaces

被引：7

作者：

Gabor, Grzegorz ^{[1
]}

机构：

[1] Nicholas Copernicus Univ, Fac Math & Comp Sci, Chopina 12-18, PL-87100 Torun, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 440卷 / 02期

关键词：

Dirichlet problem; State-dependent impulses; BVP; Billiard; EXISTENCE;

D O I：

10.1016/j.jmaa.2016.03.072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The constrained Dirichlet boundary value problem x = f(t,x), x(0) = x(T), is studied in billiard spaces, where impacts occur in boundary points. Therefore we develop the research on impulsive Dirichlet problems with state-dependent impulses. Inspiring simple examples lead to an approach enabling to obtain both the existence and multiplicity results in one dimensional billiards. Several observations concerning the multidimensional case are also given. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：677 / 691

页数：15

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