On nonoscillatory solutions of Emden-Fowler dynamic systems on time scales

Oscillation for a Class of Second-Order Emden-Fowler Delay Dynamic Equations on Time Scales

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations rxΔ Δ t p t x τ t 0 on a time scale T; here γ is a quotient of odd positive integers with r and p as real-valued positive rd-continuous functions defined on T. Our results in this paper not only extend the results given in Agarwal et al. 2005 , Akin-...

Oscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

Wewill establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations r t x t − a t x τ t ΔΔ Δ p t x δ t 0 on a time scale T, where γ > 0 is a quotient of odd positive integers with r, a, and p real-valued positive rd-continuous functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on tim...

Oscillation Criteria for Some New Generalized Emden-Fowler Dynamic Equations on Time Scales

and Applied Analysis 3 Theorem 4. Assume that (H 1 )–(H 6 ) and (7) hold. If there exists a function ξ(t) ∈ C rd(T , (0,∞)) such that for any positive numberM, lim t→∞ ∫ t t0 (ξ (s) p (s) − Q (s)) Δs = ∞, (12) where p (s) = q (s) [1 − p (δ (s))] β , Q (s) = αM(R (σ (s))) α−β r (δ (s)) ((ξ Δ (s)) + ) α+1 (α + 1) α+1 βξ (s) (δ (s)) α , (ξ Δ (s)) + := max {ξΔ (s) , 0} , (13) then (1) is oscillator...

On Nodal Solutions to Generalized Emden-fowler Equations

We introduce a new variational method in order to derive results concerning existence and nodal properties of solutions to superlinear equations, and we focus on applications to the equation where h is a Caratheodory function which is odd in u. In the particular case where h is radially symmetric, we prove, for given n 2 N, the existence of a solution having precisely n nodal domains, whereas s...

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales