On Different Type Solutions of Boundary Value Problems
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...
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Vilnius Gediminas Technical University
2016-09-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/843 |
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doaj-01d542dfa2f6453ebbbaf03ba9347dae2021-07-02T11:45:55ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102016-09-0121510.3846/13926292.2016.1204367On Different Type Solutions of Boundary Value ProblemsMaria Dobkevich0Felix Sadyrbaev1Institute of Mathematics and Computer Science, University of Latvia, Raynis boulevard 29, Riga, LatviaInstitute of Mathematics and Computer Science, University of Latvia, Raynis boulevard 29, Riga, Latvia 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]. https://journals.vgtu.lt/index.php/MMA/article/view/843boundary value problemmultiple solutionsexistence |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Maria Dobkevich Felix Sadyrbaev |
| spellingShingle |
Maria Dobkevich Felix Sadyrbaev On Different Type Solutions of Boundary Value Problems Mathematical Modelling and Analysis boundary value problem multiple solutions existence |
| author_facet |
Maria Dobkevich Felix Sadyrbaev |
| author_sort |
Maria Dobkevich |
| title |
On Different Type Solutions of Boundary Value Problems |
| title_short |
On Different Type Solutions of Boundary Value Problems |
| title_full |
On Different Type Solutions of Boundary Value Problems |
| title_fullStr |
On Different Type Solutions of Boundary Value Problems |
| title_full_unstemmed |
On Different Type Solutions of Boundary Value Problems |
| title_sort |
on different type solutions of boundary value problems |
| publisher |
Vilnius Gediminas Technical University |
| series |
Mathematical Modelling and Analysis |
| issn |
1392-6292 1648-3510 |
| publishDate |
2016-09-01 |
| description |
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].
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| topic |
boundary value problem multiple solutions existence |
| url |
https://journals.vgtu.lt/index.php/MMA/article/view/843 |
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AT mariadobkevich ondifferenttypesolutionsofboundaryvalueproblems AT felixsadyrbaev ondifferenttypesolutionsofboundaryvalueproblems |
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