On a certain approximation property for first-order abstract differential equations
On a characterization of reflexive Banach spaces
On a fixed point theorem for weakly sequentially continuous mapping
Let E be a metrizable locally convex topological vector space x ∈ E, and let D be a closed convex subset of E such that x ∈ D. In this paper we prove that the weakly sequentially continuous mapping F: D ∪ D which satisfies V̅ = c̅o̅n̅v̅({x} ∪ F(V))⇒ V is relatively weakly compact, has a fixed point. Employing the above results we prove the existence theorem for the Cauchy problem x'(t) = f(t,x(t)), x(0) = x₀. As compared with the previous...
On an inverse scattering problem for a discontinuous Sturm-Liouville equation with a spectral parameter in the boundary condition.
On Apery's differential operator
On where has infinitely many “bumps”
On differential operators with integral conditions.
On discreteness of spectrum of a functional differential operator
We study conditions of discreteness of spectrum of the functional-differential operator on . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.
On existence of nonoscillatory solutions in forced nonlinear differential equations.
On fundamental systems for differential equations of Kamke type.
On Hill's equation with a discontinuous coefficient.
On -quasi-derivatives for solutions of perturbed general quasi-differential equations
This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of th order with complex coefficients , provided that all th quasi-derivatives of solutions of and all solutions of its normal adjoint are in and under suitable conditions on the function .
On linear differential equations with transformed argument solvable by means of right invertible operators
On measures of noncompactness in topological vector spaces
On minimizing the sum of squares of norms of differential operators under constraints
On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem.
On random boundary value problems for ordinary differential equations
On regularity at t = 0 for semilinear ADEs and its numerical applications.
On some applications of Bochner-Schoenberg-Eberlein type theorems
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...