Related papers: The mean value problem of Smale's problems
We find the general form of supersymmetric invariant two point functions. By imposing supersymmetric positivity we obtain the general supersymmetric K\"allen-Lehmann representation.
We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
This paper studies the existence of minimal solutions to two-point boundary value problems for quasi-monotone dynamical systems. Specifically, the pointwise infimum of all supersolutions is shown to coincide with the minimal solution. This…
A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a…
We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.
This paper deals with more refinements of inequalities related to deviations from Mean Value involving superquadratic and uniformly convex functions.
We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes. The latter have applications to…
We consider a Riemann boundary value problem for monogenic functions in a two-dimensional commutative associative Banach algebra. We prove theorems on the existence of a solution to this problem under different assumptions on the…
In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…
We prove that outside of a closed singular set of measure zero solutions to the second boundary value problem for generated Jacobian equations are smooth.
We investigate various mean value problems involving order three primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central values of the Dirichlet L-functions associated to this family,…
We give improved lower bounds for the number of solutions of some $S$-unit equations over the integers, by counting the solutions of some associated linear equations as the coefficients in those equations vary over sparse sets. This method…
We establish a Schn$\ddot{\text{u}}$rer's convergence result and then apply it to obtain the existence of solutions on the second boundary value problem for a family of special Lagrangian equations
In the study of order estimation of the Riemann zeta-function $ \zeta(s) = \sum_{n=1}^\infty n^{-s} $, solving Lindel\"{o}f hypothesis is an important theme. As one of the relationships, asymptotic behavior of mean values has been studied.…
In this paper, we consider a generalized strong vector quasi-equilibrium problem and we prove the existence of its solutions by using some suxiliary results. One of the established theorems is proved by using an approximation method.
In this note, we extend to a composite modulo a recent result of Chan (2016) dealing with mean values of the product of an integer and its multiplicative inverse modulo a prime number.
In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…
An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described.…