Add to ORKGAbstract. We consider a second order nonlinear difference equation ∆2yn = anyn+1 + f(n, yn, yn+1) , n ∈ N. (E) The necessary conditions under which there exists a solution of equation (E) which can be written in the form yn+1 = αnun + βnvn, are given. Here u and v are two linearly independent solutions of equation ∆2yn = an+1yn+1, ( lim n→∞ αn = α < ∞ and lim n→∞ βn = β <∞). A special case of equation (E) is also considered. 1
AbstractIn this note we study the difference equationxn+1=1+xn−1xn,n=0,1,…, where initial values x−1...
We study a nonlinear second-order difference equation which considerably extends some equations in t...
The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2)...
summary:We consider a second order nonlinear difference equation \[ \Delta ^2 y_n = a_n y_{n+1} + f(...
We study the difference equation xn+1=α−xn/xn−1, n∈ℕ0, where α∈ℝ and where x−1 and x0 are so chosen ...
We study the difference equation xn+1 = α − xn/xn−1, n ∈ N0, where α ∈ R and where x−1 and x0 are so...
Abstract We present some interesting facts connected with the following second-order difference equa...
We present a representation of well-defined solutions to the following nonlinear second-order differ...
AbstractIt is known that if Σ∞j∣pj∣<∞, then the difference equation Δ2yn−1 = pnyn, n = 1,|, has solu...
AbstractNecessary and sufficient conditions are obtained for existence of positive solutions of a no...
on his 70th birthday anniversary Abstract. We give some existence results for bounded solutions of l...
AbstractThe authors consider the difference equations (*)Δ(anΔxn)=qnxn+1 and (**)Δ(anΔxn)=qnf(xn+1) ...
AbstractSome new results are obtained for the asymptotic behavior of the following second-order nonl...
AbstractIn this paper, several necessary and/or sufficient conditions are given for the existence of...
AbstractIn this paper we are dealing with the oscillatory and asymptotic behaviour of solutions of s...
AbstractIn this note we study the difference equationxn+1=1+xn−1xn,n=0,1,…, where initial values x−1...
We study a nonlinear second-order difference equation which considerably extends some equations in t...
The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2)...
summary:We consider a second order nonlinear difference equation \[ \Delta ^2 y_n = a_n y_{n+1} + f(...
We study the difference equation xn+1=α−xn/xn−1, n∈ℕ0, where α∈ℝ and where x−1 and x0 are so chosen ...
We study the difference equation xn+1 = α − xn/xn−1, n ∈ N0, where α ∈ R and where x−1 and x0 are so...
Abstract We present some interesting facts connected with the following second-order difference equa...
We present a representation of well-defined solutions to the following nonlinear second-order differ...
AbstractIt is known that if Σ∞j∣pj∣<∞, then the difference equation Δ2yn−1 = pnyn, n = 1,|, has solu...
AbstractNecessary and sufficient conditions are obtained for existence of positive solutions of a no...
on his 70th birthday anniversary Abstract. We give some existence results for bounded solutions of l...
AbstractThe authors consider the difference equations (*)Δ(anΔxn)=qnxn+1 and (**)Δ(anΔxn)=qnf(xn+1) ...
AbstractSome new results are obtained for the asymptotic behavior of the following second-order nonl...
AbstractIn this paper, several necessary and/or sufficient conditions are given for the existence of...
AbstractIn this paper we are dealing with the oscillatory and asymptotic behaviour of solutions of s...
AbstractIn this note we study the difference equationxn+1=1+xn−1xn,n=0,1,…, where initial values x−1...
We study a nonlinear second-order difference equation which considerably extends some equations in t...
The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2)...