Related papers: About a conjecture on difference equations in quas…

This paper investigates two classes of quasilinear and essentially nonlinear integral equations with a sum-difference kernel on the half-line. Such equations arise in various areas of physics, including the theory of radiative transfer in…

For a general class of divergence type quasi-linear degenerate parabolic equations with measurable coeffcients and lower order terms from non-linear Kato-type classes, we prove local boundedness and continuity of solutions, and the…

By exploiting a recently developed connection between Heun's differential equation and the generalized associated Lam\'e equation, we not only recover the well known periodic solutions, but also obtain a large class of new, quasi-periodic…

This paper deals with bounded solutions of quasilinear elliptic equations on Riemannian manifolds satisfying special condition.

The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used…

In this paper we prove the Riemann Hypothesis. More precisely, we study a Salem-type linear Fredholm integral equation of the first kind with symmetric kernel and prove that, in the class of bounded and measurable functions, this equation…

This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…

We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate the well-posedness and convergence of the truncated Carleman…

After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical…

In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion algebra. We established correspondence…

We provide elementary and accurate numerical solutions to the differential-difference equation, which improves an explicit version of the linear sieve given by Nathanson.

We solve two conjectures of Ceken-Palmieri-Wang-Zhang concerning discriminants and give some applications.

Assuming Calabi symmetry, we prove that a numerical condition ensures the solvability of the complex Hessian quotient equation, as conjectured by Sz\'ekelyhidi. We also propose a conjecture on the existence of a $k$-subharmonic…

Spaces of quasi-analytic classes are defined by the existence and uniqueness of Taylor expansions, which are not necessarily convergent. First examples were given by Borel in his theory of monogenic functions, a generalisation of…

In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…

We show that in the category of analytic sheaves on a complex analytic space, the full subcategory of quasi-coherent sheaves is an abelian subcategory.

The article develops techniques for solving equations G(x,y)=0, where G(x,y)=G(x_1,...,x_n,y) is a function in a given quasianalytic class (for example, a quasianalytic Denjoy-Carleman class, or the class of infinitely differentiable…

In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…

In this paper we prove a uniqueness result for the Calder\'{o}n problem for the quasilinear conductivity equation on a bounded domain $\R^2$. The proof of the result is based on the higher order linearization method, which reduces the…