6533b85dfe1ef96bd12bde32
RESEARCH PRODUCT
On Different Type Solutions of Boundary Value Problems
Felix SadyrbaevMaria Dobkevichsubject
Discrete mathematicsmultiple solutionsexistence010103 numerical & computational mathematicsType (model theory)01 natural sciences010101 applied mathematicsSet (abstract data type)Modeling and Simulationboundary value problemQA1-939Interval (graph theory)Boundary value problem0101 mathematicsAnalysisMathematicsMathematicsdescription
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].
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-09-20 | Mathematical Modelling and Analysis |