Related papers: Regularity of the extremal solutions in a Gelfand …
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution…
The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…
We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield,…
We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H2 of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and…
The coupling constants of fixed points in the $\epsilon$ expansion at one loop are known to satisfy a quadratic bound due to Rychkov and Stergiou. We refer to fixed points that saturate this bound as extremal fixed points. The theories…
We consider singular quasilinear elliptic systems with homogeneous Dirichlet boundary condition. Using Leray-Schauder topological degree, combined with the sub-supersolutions method and suitable truncation arguments, we establish the…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
We study the general problem of extremality for metric Diophantine approximation on submanifolds of matrices. We formulate a criterion for extremality in terms of a certain family of algebraic obstructions and show that it is sharp. In…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.
In this paper, we obtain order estimates for the Gelfand widths of intersections of finite-dimensional balls under some conditions on parameters.
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…
We obtain uniform in time $L^\infty$-bounds for the solutions to a class of thermo-diffusive systems. The nonlinearity is assumed to be at most sub-exponentially growing at infinity and have a linear behavior near zero.
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the…