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Nonoscillation theorems for forced second order non linear differential equations

John R. Graef;  Paul W. Spikes — 1975

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Gli Autori provano alcuni nuovi criteri sufficienti, indipendenti da altri criteri da loro ottenuti in precedenza, perché gli integrali dell'equazione ( a ⁢ ( t ) ⁢ x ′ ) ′ + q ⁢ ( t ) ⁢ f ⁢ ( x ) ⁢ g ⁢ ( x ′ ) = r ⁢ ( t ) siano tutti non oscillatori.

Classification of nonoscillatory solutions of higher order neutral type difference equations

Ethiraju Thandapani;  P. Sundaram;  John R. Graef;  A. Miciano;  Paul W. Spikes — 1995

Archivum Mathematicum

The authors consider the difference equation Δ m [ y n - p n y n - k ] + δ q n y σ ( n + m - 1 ) = 0 ( * ) where m ≥ 2 , δ = ± 1 , k ∈ N 0 = { 0 , 1 , 2 , ⋯ } , Δ y n = y n + 1 - y n , q n > 0 , and { σ ( n ) } is a sequence of integers with σ ( n ) ≤ n and lim n → ∞ σ ( n ) = ∞ . They obtain results on the classification of the set of nonoscillatory solutions of ( * ) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included.

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