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46.562  Articles
1 of 4.657 pages  |  10  records  |  more records»
We formulate a criterion of uniqueness of solutions of a Cauchy problem using the comparison function of the Kamke type. This will be a generalization of classical results concerning first order equations with partial derivatives. We prove that the unique... see more

The method of argument functions has become famous for solving problems of continuum mechanics. The solution of problems of the elasticity theory in polar coordinates was the further development of this method. The same approaches are applied to solving p... see more

We present existence theorems for coupled systems of quadratic integral equations of fractional order. As applications we deduce existence theorems for twocoupled systems of Cauchy problems. Also, an example illustrating the existence theorem is given.DOI... see more

In this paper we prove the existence and the uniqueness of the classical solution of non-autonomous inhomogeneous boundary Cauchy problems, and that this solution is given by a variation of constants formula. This result is applied to show the existence o... see more

The study of differential-algebraic boundary value problems was initiated in the works of K. Weierstrass, N.N. Luzin and F.R. Gantmacher. Systematic study of differential-algebraic boundary value problems is devoted to the work of S. Campbell, Yu.E. Boyar... see more

The article proposes unusual regularization conditions as well as a scheme for finding solutions of the linear Cauchy problem for a system of difference equations in the critical case, significantly using the Moore-Penrose matrix pseudo-inversion technolo... see more

The study of differential-algebraic boundary value problems was initiated in the works of K. Weierstrass, N. N. Luzin and F. R. Gantmacher. Systematic study of differential-algebraic boundary value problems is devoted to the work of S. Campbell, Yu. E. Bo... see more

In this paper, the ability of the multilayer perceptron neural network (MLP) in interpolation was used to analyze two classes of boundary value problems. The first class is formed by differential equations, with solutions which can have high gradients and... see more

Cauchy integral method has been applied to derive exact and closed expressions for Goursat's functions for the first and second fundamental problems for the infinite plate weakened by a hole having arbitrary shape.The plate considered are conformally mapp... see more

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