On Different Type Solutions of Boundary Value Problems

    Maria Dobkevich Affiliation
    ; Felix Sadyrbaev Affiliation


We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].

Keyword : boundary value problem, multiple solutions, existence

How to Cite
Dobkevich, M., & Sadyrbaev, F. (2016). On Different Type Solutions of Boundary Value Problems. Mathematical Modelling and Analysis, 21(5), 659-667.
Published in Issue
Sep 20, 2016
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.