1 - 10 of 16 articles
We consider the one-dimensional Schrödinger operator with integrable potential. We analyze the rate of the uniform equiconvergence of the biorthogonal expansion of an absolutely continuous function in the root functions of this operator with its Fourier trigonometric series on a compact set. For...
For a system of differential equations with a cylindrical phase space, we obtain conditions for the existence of several limit cycles of the second kind. These results are applied to phase synchronization systems.
We develop the method devised in the case of differential operators by V.A. Sadovnichii and V.A. Vinokurov for constructing asymptotic formulas of arbitrary-order accuracy for the eigenvalues and eigenfunctions in the case where the differential operator has an integrable potential.
We consider boundary value problems for the differential equations Δ2
u + B
u = 0 with operator coefficients B corresponding to initial-boundary value problems for the diffusion equation Δ3
u − pu = ∂
u (p > 0) on a right cylinder with inhomogeneous boundary conditions on the lateral surface...
We consider a boundary value problem for the heat equation in the exterior of a bounded domain of space variables. On the boundary of the domain, we pose a nonlinear boundary condition. We find sharp nonlinearity exponents for which there exists no global solution.
We consider a system of Riemann-Liouville fractional partial differential equations with constant coefficients and obtain a general representation of solutions in a rectangular domain. The asymptotic behavior and other properties of the fundamental solution are studied.
For the class of dynamical systems considered in the paper, we use the Lyapunov direct method to prove a sufficient criterion for the exponential dichotomy in the L
2-norm. We derive equations of the subspaces realizing the dichotomy in the phase space coordinate system associated with the...
We consider elliptic operators on stratified manifolds with stratification of arbitrary length. Under some (symmetry-like) conditions imposed on the symbols of these operators, we obtain index formulas in which the index of an operator is expressed as the sum of indices of some (explicitly...
We analyze the stability and solvability of the Cauchy problem for the equations λu
, which appear in filtration theory and are defined on a finite connected directed graph with continuity and flow balance conditions at its vertices.
We prove the strong well-posed solvability of the Cauchy problem for a second-order singular hyperbolic differential equation with variable domain of variable unbounded operator coefficients and for the mixed problem for a complete equation of string vibrations with a strong singularity in time...
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