scholarly journals The Asymptotic Behavior of Solutions of Second order Difference Equations With Damping Term

2018 ◽  
Vol 14 (2) ◽  
pp. 7806-7811
Author(s):  
Jai Kumar S ◽  
K. Alagesan
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Asymptotic Behavior Of Solutions ◽  
Damping Term ◽  
Order Difference ◽  
Keywords And Phrases ◽  
Second Order Difference Equation ◽  
Order Difference Equation

  The author presents some sufficient conditions for second order difference equation with damping term of the form                                                                             ^(an ^(xn + cxn-k)) + pn^xn + qnf(xn+1-l) = 0 An example is given to illustrate the main results. 2010 AMS Subject Classification: 39A11 Keywords and Phrases: Second order, difference equation, damping term.

scholarly journals Necessary and sufficient conditions for oscillation of second order neutral difference equations

2003 ◽  
Vol 34 (2) ◽  
pp. 137-146 ◽  
Author(s):  
E. Thandapani ◽  
K. Mahalingam
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Real Sequence ◽  
Order Difference ◽  
Neutral Difference Equations ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Necessary And Sufficient

Consider the second order difference equation of the form$\Delta^2(y\n-py_{n-1-k})+q_nf(y_{n-\ell})=0,\quad n=1,2,3,\ldots  \hskip 1.9cm\hbox{(E)}$where $ \{q_n\}$ is a nonnegative real sequence, $ f:{\Bbb R}\rightarrow {\Bbb R}$ is continuous such that $ uf(u)>0$ for $ u\not= 0$, $ 0\le p

scholarly journals Oscillation Criteria of Solution for a Second Order Difference Equation with Forced Term

2010 ◽  
Vol 2010 ◽  
pp. 1-6
Author(s):  
Chen Huiqin ◽  
Jin Zhen
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Order Difference ◽  
Oscillation Criteria ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Forced Term

We will consider oscillation criteria for the second order difference equation with forced termΔ(anΔ(xn+λxn−τ))+qnxn−σ=rn(n≥0). We establish sufficient conditions which guarantee that every solution is oscillatory or eventually positive solutions converge to zero.

Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation

2019 ◽  
Vol 20 (3-4) ◽  
pp. 433-439 ◽  
Author(s):  
Martin Bohner ◽  
Giuseppe Caristi ◽  
Shapour Heidarkhani ◽  
Shahin Moradi
Keyword(s):  
Difference Equation ◽  
Variational Methods ◽  
Sufficient Conditions ◽  
Homoclinic Solution ◽  
Second Order ◽  
Technical Approach ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractThis paper presents sufficient conditions for the existence of at least one homoclinic solution for a nonlinear second-order difference equation with p-Laplacian. Our technical approach is based on variational methods. An example is offered to demonstrate the applicability of our main results.

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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