Related papers: The mean value problem of Smale's problems
Let $\Delta(a,b;x)$ denote the error term of the general two-dimensional divisor problem. In this paper we shall study the relation between the discrete mean value $\sum_{n\leq T}\Delta^2(a,b;n)$ and the continuous mean value…
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
This paper concerns a fully nonlinear version of the Yamabe problem on manifolds with boundary. We establish some existence results and estimates of solutions.
In this paper, using combinatorial and analytic methods, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m\geq 2$. This solves a conjecture of He and Zhang [`On the $2k$-th…
We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.
We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable…
In the first part, we discuss the stability of the strong slope and of the subdifferential of a lower semicontinuous function with respect to Wijsman perturbations of the function, i.e. perturbations described via Wijsman convergence. In…
The solution of one Zamfiresku's problem was obtained. We discuss the unsolved questions related to the Mizel's problem.
In this paper various analytic techniques are com- bined in order to study the average of a product of a Hecke L- function and a symmetric square L-function at the central point in the weight aspect. The evaluation of the second main term…
In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is…
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
In this paper, we shall establish a rather general asymptotic formula in short intervals for a classe of arithmetic functions and announce two applications about the distribution of divisors of square-full numbers and integers representable…
Motivated by the mean value property of harmonic functions, we introduce the local and global median value properties for continuous functions of two variables. We show that the Dirichlet problem associated with the local median value…
Classical mean-value results of Wirsing type in analytic number theory are established under weaker than classical conditions.
In this paper we present a new solution for the Constant Astigmatism equation. This solution is parameterized by an arbitrary function of a single variable.
Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…