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Your search keyword '"Mardanov, M. J."' showing total 16 results
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16 results on '"Mardanov, M. J."'

1. Necessary conditions for a minimum in classical calculus of variation problems in the presence of various degenerations

Author

Mardanov, M. J., Melikov, T. K., and Melik, S. T.

Subjects
Mathematics - Optimization and Control
Abstract

In the paper, we offer a method for studying an extremal in the classical calculus of variation in the presence of various degenerations. This method is based on introduction of Weierstrass type variations characterized by a numerical parameter. To obtain more effective results, introduced variations are used in two forms: in the form of variations on the right with respect to the given point, and in the form of variations on the left with respect to the same point. The research is conducted under the assumption that along the considered extremal the Weierstrass condition and the Legendre condition degenerate, i.e. they are fulfilled as equalities at separate points or on some intervals. Two types of new necessary conditions are obtained: of equality type and of inequality type conditions for a strong and also a weak local minimum. Given specific examples and counterexample show that some of the necessary minimum conditions obtained in this article are strengthening and refining of the corresponding known results in this direction.

Published
2021

9. Existence and Uniqueness of Solutions for Nonlinear Fractional Integro-Differential Equations with Nonlocal Boundary Conditions.

Author

Mardanov, M. J., Sharifov, Y. A., and Aliyev, H. N.

Subjects
*INTEGRO-differential equations, *CAPUTO fractional derivatives
Abstract

In this paper, the existence and uniqueness of solutions of fractional integro-differential equations with nonlocal boundary conditions is investigated. We establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained by applying the contraction mapping principle. [ABSTRACT FROM AUTHOR]

Published
2022
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12. Existence and uniqueness of solutions for the first order non-linear differential equations with multi-point boundary conditions.

Author

Mardanov, M. J., Sharifov, Y. A., Aliyev, H. N., and Sardarova, R. A.

Subjects
*BOUNDARY value problems, *ORDINARY differential equations, *UNIQUENESS (Mathematics), *LINEAR differential equations, *LINEAR orderings, *GREEN'S functions, *INTEGRAL equations, *LINEAR systems
Abstract

This article discusses the existence and uniqueness of solutions for the system of non- linear first order ordinary differential equations with multipoint boundary conditions. The Green function is constructed, and the problem is reduced to the equivalent integral equation. Existence and uniqueness of the solution to this problem is studied using the Banach contraction mapping principle and Schaefer's fixed point theorem. [ABSTRACT FROM AUTHOR]

Published
2020
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13. Existence and Uniqueness of Solutions for Nonlinear Impulsive Differential Equations with Three-Point and Integral Boundary Conditions.

Author

Mardanov, M. J., Sharifov, Y. A., Sardarova, R. A., and Aliyev, H. N.

Subjects
*NONLINEAR differential equations, *INTEGRAL equations, *BOUNDARY value problems, *IMPULSIVE differential equations, *ORDINARY differential equations, *GREEN'S functions, *FIXED point theory
Abstract

The aim of this paper is to investigate the solution of the system of nonlinear impulsive differential equations with three-point and integral boundary conditions. The Green function is constructed and the original problem is reduced to the equivalent integral equations. Sufficient conditions are found for the existence and uniqueness of solutions to the boundary value problems for the system of first order nonlinear impul- sive ordinary differential equations with three-point and integral boundary conditions. Banach's fixed point theorem is used to prove the uniqueness and Schaefer's fixed point theorem is used to prove the existence of a solution of the considered problem. [ABSTRACT FROM AUTHOR]

Published
2020

14. Existence and uniqueness of solutions for the system of first-order nonlinear differential equations with three-point and integral boundary conditions.

Author

Mardanov, M. J., Sharifov, Y. A., Ismayilova, K. E., and Zamanova, S. A.

Subjects
*NONLINEAR differential equations, *INTEGRAL equations, *NONLINEAR systems, *ORDINARY differential equations, *GREEN'S functions, *UNIQUENESS (Mathematics)
Abstract

In the paper, the existence and uniqueness of the solutions for the system of the non-linear first-order ordinary differential equations with three-point and integral boundary conditions are studied. The Green function is constructed and the considered problem is reduced to the equivalent integral equation. The existence and uniqueness of the solutions for the given problem are analyzed by using the Banach contraction principle. The Schaefer's fixed point theorem is then used to prove the existence of the solutions. Finally, the examples are given to verify the given theorems. [ABSTRACT FROM AUTHOR]

Published
2019
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