The nonuniqueness of a regular or singular Cauchy problem for ordinary differential equations is studied in several papers such as [3, 4, 5, 13, 14, 15, 16, 17]. Most of these results can also be found in the monograph [1]. The uniqueness of solutions of Cauchy initial value problem for ordinary differential equations with singularity is investigated in [7, 8, 9, 12]. The topological structure ...

Properties of the Cauchy–Riemann–Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3–surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy– Riemann–Fueter equation are established.

let h be an infinite--dimensional hilbert space and k(h) be the set of all compact operators on h. we will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher jordan derivation on k(h) associated with the following cauchy-jencen type functional equation 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).

This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space H

where m is the normalized Lebesgue measure on T. By the Fatou Theorem, Kf can also be defined on T by its non-tangential boundary values. After such an extension one can view the Cauchy integral as a “transform”, i.e., an operator in L(m) which sends f into the boundary values of Kf . It is well known, and not difficult to see, that the Cauchy transform is unbounded for p = 1 or p = ∞. However,...

The usual domains for Cauchy distributions have been straight lines and unit circles. These domains are closed under arbitrary changes in location and scale, whether done sequentially or simultaneously. Such closure properties have been extended to spherical Cauchy distributions. Higher dimensional Cauchy based domains are created herein for unit hyperspheres and sets of straight lines of arbit...

We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...

This paper is concerned with the Cauchy problem of $2$D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness Sobolev space $H^s({\mathbb{R}}^2)$ for $s > -1/4$, and these are optimal up to endpoint. utilize nonlinear version classical Loomis-Whitney inequality develop an almost orthogonal decomposition set resonant frequencies. As a corollary, we obt...

Analytic functions in tubes in association with ultradistributional boundary values are analyzed. Conditions are stated on the analytic functions satisfying a certain norm growth which force the functions to be in the Hardy space H2 . Properties of the Cauchy kernel and Cauchy integral are obtained which extend results obtained previously by the author and collaborators.

In this paper we introduce and investigate I2-convergence, I∗ 2 -convergence, I2-limit points, and I2-cluster points of a double sequence in a fuzzy 2-normed linear space. We prove a decomposition theorem for I2-convergence of double sequences. The notions of I2-double Cauchy and I∗ 2 -double Cauchy sequence are defined, and some of their properties are studied.