Related papers: Set-theoretic problems concerning Lindelof spaces
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
We find the complete rational homology for the finite subset spaces of a $d$-dimensional sphere. We also determine the integral homology in top $d$ degrees and obtain a partial description of it in codimension $d$.
We solve a problem about the orthogonal complement of the space spanned by restricted shifts of functions in $L^2[0,1]$ posed by M.Carlsson and C.Sundberg.
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…
In this paper, we are concerned with stable solutions , possibly unbounded and sign-changing, of some semi-linear elliptic problem with mixed nonlinear boundary conditions. We establish the nonexistence of stable solutions, the main methods…
The existence, uniqueness and uniformly estimates for solutions of the parameter dependent abstract Navier-Stokes problem on half space are derived. In application the existence, uniqueness and uniformly L^{p} estimates for solution of the…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that…
We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
The question whether there is a Lindelof Q-set space or Lindelof $\Delta$-set space is considered. We show that J. Moore's ZFC $L$-space is not a Q-set space in ZFC and, assuming all Aronszajn trees are special, it is not a $\Delta$-set…
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
In this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions. By means of variational methods and an…
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
We analyze fine properties of solutions to quasilinear elliptic equations with double phase structure and characterize, in the terms of intrinsic Hausdorff measures, the removable sets for H\"older continuous solutions.
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse…