Dirichlet problem in one-dimensional billiard space with velocity dependent right-hand side
The paper brings multiplicity results for a Dirichlet problem in one-dimensional billiard space with right-hand side depending on the velocity of the ball, i.e. a problem in the form x'' = f(t, x, x') if x(t) ∈ int K, x'(t+) = -x'(t-) if x(t) ∈ ∂K, ...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2024-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://ojs.test/index.php/LMR/article/view/37775 |
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| Summary: | The paper brings multiplicity results for a Dirichlet problem in one-dimensional billiard space with right-hand side depending on the velocity of the ball, i.e. a problem in the form
x'' = f(t, x, x') if x(t) ∈ int K, x'(t+) = -x'(t-) if x(t) ∈ ∂K,
x(0) = A, x(T) = B,
where T > 0, K = [0, R], R > 0, f is a Carathéodory function on [0, T] × K × ℝ, A, B ∈ int K. Sufficient conditions ensuring the existence of at least two solutions having prescribed number of impacts with the boundary of the billiard table K are obtained. In particular, if the right-hand side has at most sublinear growth in the last variable, there exist infinitely many solutions of the problem.
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| ISSN: | 0132-2818 2335-898X |