On a boundary value problem
Abstract
The equation x"(t) = f(t,x(α(t)), x'(β(t))) for t∈[a,b], where the functions α, β deviated argument of type [a,b] → [a,b] is considered.
A sufficient condition for existence of the end b of the interval [a,b], such that there exists the solution x of the above equation on [a,b] fulfilling the boundary value conditions x(a) = A, x(b) = B and ‖x'(a)‖ = v > 0, where the constants a, v and vectors A, B are given, is proved.
References
2. J. Kalinowski, On the convergence of an iterative sequence to the solution of a system of ordinary differential equations with deviated arguments, Demonstratio Math. 9 No 1 (1976), 77-93.
3. C.A. Vavilov, Solvability a class of boundary value problems, Dokl. Akad. Nauk SSSR 305 No 2 (1989), (in Russian) 268-270.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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