On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

Authors:	Půža B

Institution:	B. Pa

Abstract:	Sufficient conditions of solvability and unique solvability of the boundary value problem $\begin{gathered} u^{\left( m \right)} (t) = f(t,u(\tau _{11} (t)), \ldots ,u(\tau _{1k} (t)), \ldots ,u^{(m - 1)} (\tau _{m1} (t)), \ldots \hfill \\ \ldots ,u^{(m - 1)} (\tau _{mk} (t))),u(t) = 0,for t \notin \left {a,b} \right], \hfill \\ u^{\left( {i - 1} \right)} (a) = 0(i = 1, \ldots ,m - 1), \ldots ,u^{(m - 1)} (b) = 0, \hfill \\ \end{gathered}$ are established, where $\tau _{ij} :\left {a,b} \right] \to R \left( {i = 1, \ldots ,m;j = 1, \ldots ,k} \right)$ are measurable functions and the vector function $f:\left] {a,b} \right \times R^{kmn} \to R^n$ is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

Keywords:	Differential equation with deviating arguments two-point singular boundary value problem existence theorem uniqueness theorem
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