Related papers: On the Boundedness of Solutions of a Rational Syst…
This expository paper is concerned with the rationality problems for three-dimensional algebraic varieties with a conic bundle structure. We discuss the main methods of this theory. We sketch the proofs of certain principal results, and…
Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift
Some boundedness properties of function spaces (considered as topological groups) are studied.
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
We investigate the existence and multiplicity of solutions for fourth order discrete boundary value problems via critical point theory.
Fishburn developed an algorithm to solve a system of $m$ difference constraints whose $n$ unknowns must take values from a set with $k$ real numbers [Solving a system of difference constraints with variables restricted to a finite set,…
We give a uniform estimate and an inequality for solutions of an equation with Dirichlet boundary condition.
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficients is studied in a rectangular domain. The existence and…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime $p$. In particular, we obtain nontrivial results about the number of solution in boxes with the side…
This paper addresses the problem of deciding the lower-boundedness of an arbitrary real polynomial p in n variables.
We examine the solubility of a diagonal, translation invariant, quadratic equation system in arbitrary (dense) subsets A \subset Z and show quantitative bounds on the size of A if there are no non-trivial solutions. We use the circle method…
The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild…
We consider an elliptic system with regular H{\"o}lderian weight and exponential nonlinearity or with weight and boundary singularity, and, Dirichlet condition. We prove the boundedness of the volume of the solutions to those systems on the…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.