1 - 10 of 14 articles
We obtain shift formulas for the root functions of odd-order differential operators with nonsmooth coefficients (an exact formula for first-order operators and an asymptotic formula for operators of higher odd order); these formulas are needed when studying the convergence of spectral expansions...
We consider the Cauchy problem for a system of two linear ordinary differential equations with two independent small parameters multiplying the derivatives. Estimates for the terms in the asymptotic expansion of the solution are obtained. Recursion formulas for the efficient computation of terms...
We study the problem on the existence of extremals with given boundary conditions for the functional I(l) = ∫
2 + qy′
2 + rz′
dt under various assumptions about the functions p, q, r ∈ C
We prove Theorem 2 stated in the first part of the paper.
We study a Cauchy type problem for a differential equation containing a fractional Riemann-Liouville partial derivative of order α, 0 < α < 2. Conditions under which the solution of the problem tends to zero as |x| → ∞ are obtained. We prove an existence theorem for a classical solution of the...
We establish the solvability of the Cauchy problem for evolution equations with Gel’fond-Leont’ev generalized differentiation operators in spaces of the type W as well as in spaces of generalized functions (analytic functionals) of the type W′.
We study the well-posedness of the mixed problem for hyperbolic equations with constant coefficients and with characteristics of variable multiplicity. We single out a class of higher-order hyperbolic operators with constant coefficients and with characteristics of variable multiplicity, for...
For a class of evolution systems of the parabolic type with unbounded coefficients, we study the properties of the fundamental solution matrices and establish the well-posed solvability of the Cauchy problem for these systems in spaces of distributions similar to Gevrey ultradistributions. For a...
The Frankl problem without the spectral parameter was considered by Bitsadze and Smirnov. The present paper gives the eigenvalues and eigenfunctions of the Frankl problem with the odd parity condition. We prove the completeness of eigenfunctions. The Frankl problem with a nonlocal parity...
We study the behavior of dynamic processes in a mathematical predator-prey model and show that the dynamical system may have a periodic solution whose period coincides with the delay. By the bifurcation method for stability analysis of periodic solutions, we establish that this periodic solution...
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