arXiv subjects
Publications and source records attributed to Marko Kostic.
In this paper, we introduce the notions of $f$-frequent hypercyclicity and ${\mathcal F}$-hypercyclicity for $C$-distribution semigroups in separable Fréchet spaces. We particularly analyze the classes of $q$-frequently hypercyclic $C$-distribution semigroups ($q\geq 1$) and frequently hypercyclic $C$-distribution semigroups, providing a great number of illustrative examples.
In this note, we analyze frequently hypercyclic solutions of abstract higher-order differential equations in separable infinite-dimensional complex Banach spaces. We essentially apply results from the theory of $C$-regularized semigroups, providing several illustrative examples and possible applications.
In the paper under review, we construct complex powers of multivalued linear operators with polynomially bounded $C$-resolvent existing on an appropriate region of the complex plane containing the interval $(-\infty,0].$ In our approach, the operator $C$ is not necessarily injective. We clarify the basic properties of introduced powers and analyze the abstract incomplete fractional differential inclusions associated with the use of modified Liuoville right-sided derivatives. We also consider abstract incomplete differential inclusions of second order, working in the general setting of sequentially complete locally convex spaces. Our results seem to be completely new even in the Banach space setting.
In this paper, we are primarily concerned with the study of entire and analytical solutions of abstract degenerate (multi-term) fractional differential equations with Caputo time-fractional derivatives. We also analyze systems of such equations and furnish several illustrative examples to demonstrate usage of obtained theoretical results.
The main aim of this paper is to investigate Weyl-$p$-almost periodic properties and asymptotically Weyl-$p$-almost periodic properties of convolution products. In such a way, we continue several recent research studies of ours which do concern a similar problematic.
In this paper, we analyze the existence and uniqueness of generalized weighted pseudo-almost automorphic solutions of abstract Volterra integro-differential inclusions in Banach spaces. The main results are devoted to the study of various types of weighted pseudo-almost periodic (automorphic) properties of convolution products. We illustrate our abstract results with some examples and possible applications.
The main aim of this paper is to investigate almost periodicity and asymptotic almost periodicity of abstract semilinear Cauchy inclusions of first order with (asymptotically) Stepanov almost periodic coefficients. To achieve our goal, we employ fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularites at zero.
In this paper, we examine various types of ${\mathcal F}$-hypercyclic (${\mathcal F}$-topologically transitive) and disjoint ${\mathcal F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.
The main purpose of this paper is to introduce the notion of an asymptotically almost periodic ultradistribution and asymptotically almost automorphic ultradistribution with values in a Banach space, as well as to further analyze the classes of asymptotically almost periodic and asymptotically almost automorphic distributions with values in a Banach space. We provide some applications of the introduced concepts in the analysis of systems of ordinary differential equations.
In the paper under review, we analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularites at zero. Our results are well illustrated and seem to be not considered elsewhere even for fractional relaxation equations with almost sectorial operators.