1 - 10 of 17 articles
We consider families of linear differential systems continuously depending on a real parameter. The stability (respectively, asymptotic stability) set of such a family is defined as the set of all values of the parameter for which the corresponding systems in the family are stable (respectively,...
We study whether it is necessary to require the estimates for the norms of solutions in the definition of an exponentially dichotomous system to be uniform.
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 suggest a method that permits one to locate limit cycles of planar vector fields with a weak focus. We use this method to analyze a large domain on the phase plane for the Shi Songling equation. The limit cycles in a neighborhood of the singular point (0, 0) are located in narrow annuli, in...
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
We consider a boundary value problem in a model domain periodically perforated along the boundary. We assume that the homogeneous Neumann condition is posed on the external boundary and the homogeneous Dirichlet condition is posed on the boundary of the cavities. A limit (homogenized) problem is...
In a weighted space, we find sufficient conditions for the normal solvability of a boundary value problem for a class of fourth-order operator-differential equations whose leading part has multiple characteristics. Note that these conditions are expressed in terms of properties of operator...
We use the method of energy inequalities and averaging operators with variable step to prove the existence and uniqueness of a strong solution of boundary value problems for a fourth-order equation of composite type.
The present paper deals with differential equations with edge degeneration in spaces with asymptotics. We give the definition of an edge space with asymptotics, prove the continuity of operators with edge degeneration in the scale of these spaces, present statements of problems with edge...
We consider the behavior of solutions in unbounded domains as |x| → ∞ and in a neighborhood of an isolated singular point for a class of nonlinear elliptic equations and inequalities degenerating with respect to the coordinate variable, the solution, and the solution gradient.
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