A pr 1 99 9 Asymptotic Behavior of Positive Solutions of the Equation ∆ u + Ku n + 2 n − 2 = 0 in IR n and Positive Scalar

BEHAVIOR OF SOLUTIONS TO A FUZZY NONLINEAR DIFFERENCE EQUATION

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

Some Compactness Results Related to Scalar Curvature Deformation

Motivated by the prescribing scalar curvature problem, we study the equation ∆gu+Ku p = 0 (1 + ζ ≤ p ≤ n+2 n−2 ) on locally conformally flat manifolds (M, g) with R(g) = 0. We prove that when K satisfies certain conditions and the dimension of M is 3 or 4, any solution u of this equation with bounded energy has uniform upper and lower bounds. Similar techniques can also be applied to prove that...

The Scalar Curvature Deformation Equation on Locally Conformally Flat Manifolds

Abstract. We study the equation ∆gu− n−2 4(n−1)R(g)u+Ku p = 0 (1+ ζ ≤ p ≤ n+2 n−2 ) on locally conformally flat compact manifolds (M, g). We prove the following: (i) When the scalar curvature R(g) > 0 and the dimension n ≥ 4, under suitable conditions on K, all positive solutions u have uniform upper and lower bounds; (ii) When the scalar curvature R(g) ≡ 0 and n ≥ 5, under suitable conditions ...

0 Growth Estimates on Positive Solutions of the Equation ∆ u + Ku n + 2 n − 2 = 0 in IR n Man Chun L EUNG

Asymptotic behavior of a system of two difference equations of exponential form

In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $E=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...