On Different Type Solutions of Boundary Value Problems*. Issue 5 (2nd September 2016)

• Record Type: Journal Article
• Authors: Dobkevich, Maria; Sadyrbaev, Felix
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 5(2016)
• Page Start: 659
• Page End: 667
• Publication Date: 2016-09-02
• Subjects: boundary value problem -- multiple solutions -- existence; 34B15; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1204367
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: We consider boundary value problems of the type xʺ = f ( t, x, xʹ ), ( ∗ ) 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 ʺ = fx ( t, ξ ( t ), ξʹ ( t )) y + fxʹ ( t, ξ ( t ), ξʹ ( t )) yʹ, y ( a ) = 0, yʹ (a) = 1, has exactly i zeros in the interval ( a, b ) and y ( b ) ≠ 0. Suppose there exist two solutions x 1 ( t ) and x 2 ( t ) of the BVP. We study properties of the set S of all solutions x ( t ) of the equation (∗) such that x ( a ) = A, xʹ1 ( a ) ≤ xʹ (a) ≤ xʹ2 ( a ) provided that solutions extend to the interval [ a, b ].