Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients

2020 ◽  
Vol 26 (7) ◽  
pp. 966-986
Author(s):  
Yuhua Long
Keyword(s):  
Difference Equation ◽  
Second Order ◽  
Functional Difference ◽  
Periodic Coefficients ◽  
Nonlinear Functional ◽  
Functional Difference Equation ◽  
Sign Changing Solutions

scholarly journals Remarks on: “Oscillation criteria for second-order functional difference equation with neutral terms” [Demonstratio Math. 41 (2008)]

2009 ◽  
Vol 42 (3) ◽  
Author(s):  
Başak Karpuz
Keyword(s):  
Difference Equation ◽  
Second Order ◽  
Functional Difference ◽  
Oscillation Criteria ◽  
Counter Example ◽  
Functional Difference Equation

AbstractIn this paper, we show that the paper mentioned in the title includes some wrong results. We also provide a counter example.

Oscillation criteria for second-order functional difference equation with neutral terms

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Yaşar Bolat
Keyword(s):  
Difference Equation ◽  
Second Order ◽  
Functional Difference ◽  
Oscillation Criteria ◽  
Functional Difference Equation

AbstractIn this manuscript, two type of new oscillation criteria are obtained respect to coefficient

scholarly journals Oscillation of a Class of Third Order Generalized Functional Difference Equation

2018 ◽  
Author(s):  
P.Venkata Mohan Reddy ◽  
Adem Kilicman ◽  
Maria Susai Manuel
Keyword(s):  
Difference Equation ◽  
Sufficient Conditions ◽  
Functional Difference ◽  
Third Order ◽  
Oscillation Criteria ◽  
Functional Difference Equation

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

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