In this note, we prove weighted resolvent estimates for the semiclassical Schrodinger operator $-h^2 \Delta + V(x) : L^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$, $n \neq 2$. The potential $V$ is real-valued, and assumed to either decay at infinity or obey a radial $\alpha$-Holder continuity condition, $0\leq \alpha \leq 1$, with sufficient of local $C^\alpha$ norm toward infinity. Note, however, t...

In this study we give solutions for the following difference equation sytem 
 x_{n+1}= (a.x_{n}y_{n-3}/y_{n-2}-\alpha)+\beta y_{n+1}=(b.x_{n-3}y_{n}/x_{n-2}-\beta) +\alpha n ∈N0
 where parameters a,b,, and initial values x_{-i}, y_{-i}, i=0,1,2,3 are non-zero real numbers. We show asymptotic behavior of system equation.

A spacelike surface in Minkowski space $\mathbb{R}_1^3$ is called a $K^{\alpha}$-translator of the flow by powers Gauss curvature if satisfies $K^{\alpha} = \langle N, \vec{v} \rangle$, $\alpha \neq 0$, where $K$ curvature, $N$ unit normal vector field and $\vec{v}$ direction $\mathbb{R}_1^3$. In this paper, we classify all rotational $K^{\alpha}$-translators. This classification will depend on...

We introduce and analyze a novel type of coalescent processes called cross-multiplicative that models system with two types particles, $A$ $B$. The bonds are formed only between the pairs particles opposite same rate for each bond, producing connected components made both types. solve Smoluchowski coagulation equations obtained as hydrodynamic limit corresponding Marcus-Lushnikov process. estab...

In this paper, we study the existence of normalized ground states to following lower critical fractional Choquard equation $ (-\Delta)^su = \lambda u+\gamma(I_{\alpha}*|u|^{1+\frac{\alpha}{N}})|u|^{\frac{\alpha}{N}-1}u+\mu |u|^{q-2}u\ \mbox{in}\ \mathbb R^N under L^2 $-norm constraint$ \int_{\mathbb R^N}|u|^2dx a^2, $where N \geq3 $, s\in(0,1) \alpha\in (0,N) a, \gamma, \mu>0 and 2<q\leq ...

in this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,t)$, subject to nulldirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. the optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

Abstract We consider the 1 d one-component plasma in thermal equilibrium, consisting of N equally charged particles on a line, with pairwise Coulomb repulsion and confined by an external harmonic potential. study two observables: (i) distribution gap between consecutive bulk (ii) number I fixed interval = [− L , + ] inside bulk, so-called full-counting-statistics (FCS). For both observables, we...