Multiple solutions of the Dirichlet problem in multidimensional billiard spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F23%3A73614749" target="_blank" >RIV/61989592:15310/23:73614749 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11784-022-01040-w" target="_blank" >https://link.springer.com/article/10.1007/s11784-022-01040-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11784-022-01040-w" target="_blank" >10.1007/s11784-022-01040-w</a>

Result language
angličtina
Original language name
Multiple solutions of the Dirichlet problem in multidimensional billiard spaces
Original language description
Dirichlet problem in an n-dimensional billiard space is investigated. In particular, the system of ODEs x''(t)=f(t,x(t)) together with Dirichlet boundary conditions x(0)=A, x(T)=B in an n-dimensional interval K with elastic impact on the boundary of K is considered. The existence of multiple solutions having prescribed number of impacts with the boundary is proved. As a consequence the existence of infinitely many solutions is proved, too. The problem is solved by reformulating it into non-impulsive problem with a discontinuous right-hand side. This auxiliary problem is regularized and the Schauder Fixed Point Theorem is used.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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