Displaying similar documents to “One case of appearance of positive solutions of delayed discrete equations”

Oscillation theorems for third order nonlinear delay difference equations

Kumar S. Vidhyaa, Chinnappa Dharuman, Ethiraju Thandapani, Sandra Pinelas (2019)

Mathematica Bohemica

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Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form Δ ( a n ( Δ ( b n ( Δ y n ) α ) ) ) + q n f ( y σ ( n ) ) = 0 to have property ( A ) or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.

Asymptotic behaviour of solutions of third order nonlinear difference equations of neutral type

Anna Andruch-Sobiło, Andrzej Drozdowicz (2008)

Mathematica Bohemica

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In the paper we consider the difference equation of neutral type Δ 3 [ x ( n ) - p ( n ) x ( σ ( n ) ) ] + q ( n ) f ( x ( τ ( n ) ) ) = 0 , n ∈ ℕ ( n 0 ) , where p , q : ℕ ( n 0 ) → ℝ + ; σ , τ : ℕ → ℤ , σ is strictly increasing and lim n → ∞ σ ( n ) = ∞ ; τ is nondecreasing and lim n → ∞ τ ( n ) = ∞ , f : ℝ → ℝ , x f ( x ) > 0 . We examine the following two cases: 0 < p ( n ) ≤ λ * < 1 , σ ( n ) = n - k , τ ( n ) = n - l , and 1 < λ * ≤ p ( n ) , σ ( n ) = n + k , τ ( n ) = n + l , where k , l are positive integers. We obtain sufficient conditions under which all nonoscillatory solutions of the above equation tend to zero as n → ∞ with a weaker assumption on q than the usual assumption ∑ i = n 0 ∞ q ( i ) = ∞ that is used in literature.