Related papers: Existence and uniqueness theorems for functional e…
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a $\log$ mapping to Laguerre polynomials. We develop basic approximation…
In this paper we prove a version of the Fountain Theorem for a class of nonsmooth functionals that are sum of a $C^1$ functional and a convex lower semicontinuous functional, and also a version of a theorem due to Heinz for this class of…
We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
An Ito formula is developed in a context consistent with the development of abstract existence and unique- ness theorems for nonlinear stochastic partial differential equations, which are singular or degenerate. This is a generalization of…
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is…
We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of…
Identity theorem for analytic complex functions says that a function is uniquely defined by its values on a set that contains a density point. The paper presents sufficient conditions for classes of real analytic functions that ensures…
In this paper we obtain bounds for integer solutions of quadratic polynomials in two variables that represent a natural number. Also we get some results on twin prime numbers. In addition, we use linear functionals to prove some results of…
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
There are several methods for proving the existence of the solution to the elliptic boundary problem $Lu=f \text{\,\, in\,\,} D,\quad u|_S=0,\quad (*)$. Here $L$ is an elliptic operator of second order, $f$ is a given function, and…
We generalize the phenomenon of continuation from complex anal- ysis to locally operator monotone functions. Along the lines of the egde-of- the-wedge theorem, we prove continuations exist dependent only on geometric features of the domain…
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original…
Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
On even-dimensional Euclidean space for integer powers of the Laplace operator greater than or equal to half the dimension, a fundamental solution of the polyharmonic equation has binomial and logarithmic behavior. Gegenbauer polynomial…
The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are…