1 - 10 of 13 articles
For families of n-dimensional linear differential systems (n ≥ 2) whose dependence on a parameter ranging in a metric space is continuous in the sense of the uniform topology on the half-line, we obtain a complete description of the ith Lyapunov exponent as a function of the parameter for each i...
We study the existence of a conditionally periodic solution of a linear system with a Stepanov conditionally periodic inhomogeneity. We prove that if this system has a bounded solution, then almost every system in its H-class has a bounded Besicovitch conditionally periodic solution.
A comparison principle based on Minkowski mixed volumes is established for a family of differential equations with imprecise parameter values. Scalar and vector approaches are considered, and the basic inequalities of the comparison principle are established.
Quasiperiodic nonconservative perturbations of two-dimensional Hamiltonian systems are studied. The behavior of solutions in a neighborhood of resonance and nonresonance levels is considered. Conditions for the existence of resonant quasiperiodic solutions (m-dimensional resonance tori) are...
A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the...
New formulas are obtained for the principal asymptotics of bifurcation solutions in the problem on the Andronov–Hopf bifurcation, leading to new algorithms for studying bifurcations in the general setting. The approach proposed in the paper allows one to consider not only the classical problems...
The behavior of solutions of the Poisson equation on noncompact Riemannian manifolds of a special form is studied. Sharp conditions for the unique solvability of the Dirichlet problem on the reconstruction of solutions of the Poisson equation from continuous boundary data at infinity are found.
The main object of study is the stochastic Cauchy problem for a quasilinear equation with random disturbances in the form of a Hilbert-valued white noise process and with an operator generating an integrated semigroup in the space L
2(R). We use the Colombeau theory of multiplication of...
The first boundary value problem for a multidimensional parabolic differential equation with a small parameter ε multiplying all derivatives is studied. A complete (i.e., of any order with respect to the parameter) regularized asymptotics of the solution is constructed, which contains a...
We study the solvability of a new class of functional-differential equations with transformations of the arguments of the unknown function. The transformations include contractions in one independent variable and dilations in the other. (We refer to such transformations as orthotropic...
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