In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.
The aim of this paper is to deduce oscillatory and asymptotic behavior of the solutions of the ordinary differential equation L_nu(t)+p(t)u(t)=0.
The equation to be considered is The aim of this paper is to derive sufficient conditions for property (A) of this equation.
The aim of this paper is to deduce oscillatory and asymptotic behavior of delay differential equation from the oscillation of a set of the first order delay equations.
In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.
In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic -mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic -mild solution of a two-dimensional impulsive fractional...
We study pseudo-abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number of their zeros.
In this paper we give a survey on the theory of quadratic functionals. Particularly the relationships between positive definiteness and the asymptotic behaviour of Riccati matrix differential equations, and between the oscillation properties of linear Hamiltonian systems and Rayleigh’s principle are demonstrated. Moreover, the main tools form control theory (as e.g. characterization of strong observability), from the calculus of variations (as e.g. field theory and Picone’s identity), and from matrix...