George Kvinikadze

On Some Boundary Value Problems for High Order Ordinary Differential Equations

Singular boundary value problems are considered for high order nonlinear equations in the case where the right-hand side may have singularities both in independent and phase variables. Existence, uniqueness theorems are proved. A priori asymptotic estimates of solutions are obtained. The obtained problems, in the case of the second order, involve those arising while studying the flow of a viscuous fluid when written in the so-called Crocco variables.

Mathematics Subject Classification: 34B15.

Key words and phrases: Singular boundary value problem, existence, uniqueness, asymptotic estimates.