in  this paper, we investigate the generalizedhyers-ulam-rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{z}-{0,pm1}$) in $p-$banach spaces.

Real and bounded elliptic solutions suitable for applying the KhareSukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified KadomtsevPetviashvili equation (gmKPE) and the nonlinear cubic-quintic Schrödinger equation (NLCQSE).

We prove global well-posedness for the defocusing cubic wave equation

We prove global well-posedness for the defocusing cubic wave equation

We prove global well-posedness for the radial defocusing cubic wave equation

We consider the nonlinear Schrödinger equation with a focusing cubic term and defocusing quintic nonlinearity in dimensions two three. The main interest of this article is problem orbital (in-)stability ground state solitary waves. recall notions energy minimizing versus action states prove that, general, must be considered as nonequivalent. numerically investigate stability least radially symm...