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.

The nonlinear physical model such as the cubic nonlinear Schrodinger equation has been applied in many branches of physics. In this paper, the )) ( exp(    expansion method is applied to evaluate new exact travelling wave solutions of the complex Schrodinger equation with cubic nonlinearity. Various solutions of the cubic nonlinear Schrodinger equation using this method provide us the firm m...

In this paper, we find all the solutions of the Diophantine equation x + 2 513 = y in nonnegative integers x, y, α, β, γ, n ≥ 3 with x and y coprime. In fact, for n = 3, 4, 6, 8, 12, we transform the above equation into several elliptic equations written in cubic or quartic models for which we determine all their {2, 5, 13}-integer points. For n ≥ 5, we apply a method that uses primitive diviso...

We consider the large data scattering problem for 2D and 3D cubic-quintic nonlinear Schrödinger equation in focusing-focusing regime. Our attention is firstly restricted to space, where cubic nonlinearity L2-critical. establish a new type of criterion that uniquely determined by mass initial data, which differs from classical setting based on Lyapunov functional. At end, we formulate solely mas...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...