Related papers: Strongly Nonlinear Differential Equations with Car…
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type…
In this study, we deal with the sharp bounds of certain Toeplitz determinants whose entries are the logarithmic coefficients of analytic univalent functions $f$ such that the quantity $z f'(z)/f(z)$ takes values in a specific domain lying…
A non-classical differential calculus on the quantum disc and cones is constructed and the associated integral is calculated.
We study about solutions of certain kind of non-linear differential difference equations $$f^{n}(z)+wf^{n-1}(z)f^{'}(z)+f^{(k)}(z+c)=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z}$$ and…
We give complete and exact descriptions of spaces of ultradifferentiable functions that are closed under composition with either holomorphic or ultradifferentiable functions -- which are two distinct cases. The proof works by considering…
We prove in this article the well posedness of non - linear Ordinary Differential Equations (ODE) of first and second order in Orlicz spaces with unbounded domain of definition.
We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\mathbb{R}^n$, $n\ge 2$, for classes of semilinear and quasilinear conductivity equations,…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…
We define a noncommutative differential calculus constructed from the inner derivation, then several relevant examples are showed. It is of interest to note that for certain $C^*$-algebra, this calculus is closely related to the classical…
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
This paper aims at studying a functional $K$-transformation $w\left( z \right)\to \widetilde{w}\left( z \right)=w\left( z \right)K\left( z \right)$ that is made to reconsider the complex differentiability for a given complex function $w$…
The classical Rellich inequalities imply that the $L^2$-norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not…
We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. More generally, we then…
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an…
We provide explicit partial differential equations - in finite cases - and functional differential equations - in field-theoretic cases - which determine observables or beables in the senses of Kucha\v{r} and of Dirac. These cover a wide…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…