Abstract
In the paper we study the question of the solvability and unique solvability of systems of the higher order differential equations with the argument deviations \begin{equation*} u_i^{(m_i)}(t)=p_i(t)u_{i+1}(\tau _{i}(t))+ q_i(t), (i=\overline {1, n}), \text {for $t\in I:=[a, b]$}, \end{equation*} and \begin{equation*}u_i^{(m_i)} (t)=F_{i}(u)(t)+q_{0i}(t), (i = \overline {1, n}), \text {for $ t\in I$}, \end{equation*} under the conjugate $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=\overline {1, k_i}$, $j_2=\overline {1, m_i-k_i}$, $i=\overline {1, n}$, and the right-focal $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=\overline {1, k_i}$, $j_2=\overline {k_i+1,m_i}$, $i=\overline {1, n}$, boundary conditions, where $u_{n+1}=u_1, $ $n\geq 2, $ $m_i\geq 2, $ $p_i \in L_{\infty }(I; R), $ $q_i, q_{0i}\in L(I; R), $ $\tau _i\colon I\to I$ are the measurable functions, $F_i$ are the local Caratheodory's class operators, and $k_i$ is the integer part of the number $m_i/2$.In the paper are obtained the efficient sufficient conditions that guarantee the unique solvability of the linear problems and take into the account explicitly the effect of argument deviations, and on the basis of these results are proved new conditions of the solvability and unique solvability for the nonlinear problems.
Publisher
Det Kgl. Bibliotek/Royal Danish Library
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献