1 - 10 of 19 articles
We consider a spectral problem for a fourth-order ordinary differential equation with spectral parameter in a boundary condition. We study the structure of root spaces and analyze the basis properties in the space L
(0, l), 1 < p < ∞, of systems of root functions of that problem.
We obtain sufficient coefficient conditions for the unique solvability of a multipoint boundary value problem for the Lyapunov matrix differential equation in the case of strong degeneration of the boundary conditions. We suggest an efficient algorithm for constructing the solution.
We consider a one-dimensional quasilinear eigenvalue and eigenfunction problem. The simplification of the problem by replacing a second-order elliptic operator by a one-dimensional one permits carrying out an efficient and unified study of the structure of the spectrum and the multiplicity of...
We obtain conditions for the asymptotic equivalence of linear stochastic and deterministic systems and analyze the oscillation of solutions of the Itô stochastic equation of the second order of the form
$\ddot x + (p(t) + q(t)\dot W(t))x = 0$
on the half-line.
We develop a unified approach to the investigation of invariant properties of Euler and non-Euler functionals and establish a relationship of variational symmetries with first integrals of a given evolution operator equation of second order with respect to t. In addition, we investigate the...
We consider a boundary value problem for the Laplace operator in a model domain periodically perforated along the boundary. We assume that the homogeneous Neumann condition is posed on the exterior boundary and the homogeneous Dirichlet condition is posed on the boundary of the cavities. We...
We consider the Cauchy problem for the quasilinear hyperbolic system describing a one-dimensional flow of a gas with the equation of state p = p(ϱ), p′(ϱ) > 0, and with initial data satisfying a monotonicity condition. We suggest an approach to solving it by reduction to the Cauchy problem for...
We study the solvability of a boundary value problem for a quasilinear partial differential equation of the second kind. To this end, we use a variational method; namely, we prove the existence of a point of absolute minimum of a functional, and this point is a solution of the original problem.
We consider a boundary control problem for a system of second-order hyperbolic equations without the mixed derivative. The boundary functions are constructed. We state a theorem that gives existence conditions for boundary controls.
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