论文标题
多维台球空间中Dirichlet问题的多个解决方案
Multiple solutions of the Dirichlet problem in multidimensional billiard spaces
论文作者
论文摘要
调查了$ n $二维台球空间中的Dirichlet问题。尤其是，考虑到$ n $二维的间隔$ k $中的odes $ \ ddot x（t）= f（t，x（t））$以及dirichlet边界条件$ x（0）= a $ x（0）= a $，$ x（t）= b $ in $ n $二维的间隔$ k $，弹性对$ k $的边界产生了弹性影响。事实证明，存在多种解决方案的有多种解决方案。结果，也证明了许多解决方案的存在。通过将其重新制定为不连续的右侧，将其重新制定为非强烈的问题来解决问题。此辅助问题是正规化的，并使用了Schauder固定点定理。
Dirichlet problem in an $n$-dimensional billiard space is investigated. In particular, the system of ODEs $\ddot x(t) = f(t,x(t))$ 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 reformulation it into non-impulsive problem with a discontinuous right-hand side. This auxiliary problem is regularized and the Schauder Fixed Point Theorem is used.
