Alternative Cauchy equation in three unknown functions

A functional equation with two unknown functions

A Cauchy-riemann Equation for Generalized Analytic Functions

We denote by T 2 the torus: z = exp iθ, w = exp iφ, and we fix a positive irrational number α. Aα denotes the space of continuous functions f on T 2 whose Fourier coefficient sequence is supported by the lattice half-plane n + mα ≥ 0. R. Arens and I. Singer introduced and studied the space Aα, and it turned out to be an interesting generalization of the disk algebra. Here we construct a differe...

Non-Archimedean stability of Cauchy-Jensen Type functional equation

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

The Cauchy problem for the L-critical focusing Hartree equation in three dimensions

For the defocusing, energy subcritical case, J. Ginibre and G. Velo [8] proved the global well-posedness and scattering results in the energy space. Later, K. Nakanishi [25] made use of a new Morawetz estimate to obtain the similar results for the more general functions V (x). Recently, the authors proved the global wellposedness and scattering for the defocusing, energy critical Hartree equati...

The Cauchy Problem of the Ward Equation

We generalize the results of [22], [11], [8] to study the inverse scattering problem of the Ward equation with non-small data and solve the Cauchy problem of the Ward equation with a non-small purely continuous scattering data.