On the Dirichlet problem in billiard spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:440

Article

Gabor, Grzegorz¹ 

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

关键词: Dirichlet problem;    State-dependent impulses;    BVP;    Billiard;   

DOI  :  10.1016/j.jmaa.2016.03.072

来源: Elsevier

【 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.

【 授权许可】

Free