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On a two point linear boundary value problem for system of ODEs with deviating arguments

Jan Kubalčík (2002)

Archivum Mathematicum

Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments x ' ( t ) = A ( t ) x ( τ 11 ( t ) ) + B ( t ) u ( τ 12 ( t ) ) + q 1 ( t ) , u ' ( t ) = C ( t ) x ( τ 21 ( t ) ) + D ( t ) u ( τ 22 ( t ) ) + q 2 ( t ) , α 11 x ( 0 ) + α 12 u ( 0 ) = c 0 , α 21 x ( T ) + α 22 u ( T ) = c T is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.

On certain singular third order eigenvalue problem

Michal Greguš, Michal Greguš, Jr. (2003)

Archivum Mathematicum

In this paper a singular third order eigenvalue problem is studied. The results of the paper complete the results given in the papers [3], [5].

On exact solutions of a class of interval boundary value problems

Nizami A. Gasilov (2022)

Kybernetika

In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differential equations, the coefficients and the boundary values of which are constant intervals. To solve this kind of interval BVP, we implement an approach that differs from commonly used ones. With this approach, the interval BVP is interpreted as a family of classical (real) BVPs. The set (bunch) of solutions of all these real BVPs we define to be the solution of the interval BVP. Therefore, the novelty of the...

On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints

Adel Mahmoud Gomaa (2012)

Czechoslovak Mathematical Journal

We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri...

On Poisson-Dirichlet problems with polynomial data

Henryk Gzyl (2002)

Publicacions Matemàtiques

In this note we provide a probabilistic proof that Poisson and/or Dirichlet problems in an ellipsoid in Rd, that have polynomial data, also have polynomial solutions. Our proofs use basic stochastic calculus. The existing proofs are based on famous lemma by E. Fisher which we do not use, and present a simple martingale proof of it as well.

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