We solve the local Cauchy problem for the nonlinear Schrödinger equation with harmonic potential, an equation appearing in the study of Bose-Einstein condensation. We prove that the mathematical study of this equation is very close to the study of the same equation without potential, thanks to two explicit operators. We prove the analogue of the pseudo-conformal conservation law, and results fo...

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

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.

A parabolic equation or inequality in an infinite domain is considered. The lateral Cauchy data for this equation are assumed to be given at an arbitrary smooth lateral surface. An inverse problem of the interest of this paper consists in an estimate of the unknown initial condition via these Cauchy data.