Application of bounded operators and Lyapunov's majorizing equations to the analysis of differential equations with a small parameter
О существовании двусторонних решений линейных интегродифференциальных уравнений типа Вольтерра с последействием
Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect
The integrodifferential system with aftereffect (“heredity” or “prehistory”) dx/dt=Ax+-t R(t,s)x(s,)ds, is considered; here is a positive small parameter, is a constant matrix, is the kernel of this system exponentially decreasing in norm as . It is proved, if matrix and kernel satisfy some restrictions and does not exceed some bound , then the -dimensional set of the so-called principal two-sided solutions approximates in asymptotic sense the infinite-dimensional set of solutions...
Numeric-analytical construction of Mathieu functions
In this paper we present an iterative algorithm for the construction of Mathieu functions of any order in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.
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