New criteria for the oscillation and existence of monotone solutions of second-order nonlinear difference equations

2000 ◽  
Vol 114 (1) ◽  
pp. 103-114 ◽  
Author(s):  
Mingshu Peng ◽  
Weigao Ge ◽  
Qianli Xu
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Monotone Solutions ◽  
New Criteria

scholarly journals A boundary value problem for second-order nonlinear difference equations on the integers

2005 ◽  
Vol 47 (2) ◽  
pp. 237-248
Author(s):  
F. Dal ◽  
G. Sh. Guseinov
Keyword(s):  
Boundary Value Problem ◽  
Difference Equations ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Left Hand ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Limit Circle Case ◽  
Difference Expression

AbstractIn this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers Z. under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l2 and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.

MODIFIED OSCILLATION CRITERIA OF SECOND-ORDER NEUTRAL DIFFERENCE EQUATIONS

2021 ◽  
Vol 28 (1-2) ◽  
pp. 19-30
Author(s):  
G. CHATZARAKIS G. CHATZARAKIS ◽  
R. KANAGASABAPATHI R. KANAGASABAPATHI ◽  
S. SELVARANGAM S. SELVARANGAM ◽  
E. THANDAPANI E. THANDAPANI
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Nonlinear Difference Equations ◽  
Transformation Technique ◽  
Neutral Difference Equations ◽  
Oscillation Criteria ◽  
Neutral Term

In this paper we shall consider a class of second-order nonlinear difference equations with a negative neutral term. Some new oscillation criteria are obtained via Riccati transformation technique. These criteria improve and modify the existing results mentioned in the literature. Some examples are given to show the applicability and significance of the main results.

scholarly journals Oscillation criteria for certain third order nonlinear difference equations

2009 ◽  
Vol 3 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Said Grace ◽  
Ravi Agarwal ◽  
John Graef
Keyword(s):  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
New Criteria

Some new criteria for the oscillation of all solutions of third order nonlinear difference equations of the form ? (a(n)(?2 x(n))? + q(n)f (x[g(n)]) = 0 and ? (a(n)(?2 x(n))? = q(n)f (x[g(n)]) + p(n)h(x[?(n)]) ? -1/? with P a (n) < ? are established.

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