In this paper using some new dynamic inequalities we present some oscillation results for higher order dynamic equation { rn−1(t) φαn−1 [ (rn−2(t)(...(r1(t)φα1 [x (t)])...)) ]}∆ +p(t)φγ (x(g(t))) = 0, on an unbounded time scale T. Some new oscillation criteria are obtained using comparison techniques. Some applications illustrating our results are included.

Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solutions to the following third-order neutral delay functional differential equation with deviating arguments ... x (t) + aẍ(t) + g(ẋ(t− τ(t))) + f(x(t− τ(t))) = p(t). Our results complement and extend known results and are illustrated with examples.

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed ...

We give sufficient conditions so that all solutions of differential equations r t y′′ t ′ q t k y′ t p t y g t f t , t ≥ t0, and r t y′′ t ′ q t k y′ t p t h y g t f t , t ≥ t0, are nonoscillatory. Depending on these criteria, some results which exist in the relevant literature are generalized. Furthermore, the conditions given for the functions k and h lead to studying more general differentia...

We read with interest the article ‘A patient with abdominal pain and a rash’ by van Laarhoven et al. They made the diagnosis of Henoch-Schönlein purpura (HSP) in their patient using the American College of Rheumatology (ACR) criteria. Recently, however, the diagnostic criteria of HSP were modified by EULAR/PReS (the European League against Rheumatism/ Paediatric Rheumatology European Society) t...

The authors establish some new criteria for the oscillation and asymptotic behavior of all solutions of the equation. (a(t)(x(t) + p(t)x(τ(t)))) + q(t) max [σ(t),t] x(s) = 0, t ≥ t0 ≥ 0, where a(t) > 0, q(t) ≥ 0, τ(t) ≤ t, σ(t) ≤ t, α is the ratio of odd positive integers, and ∫∞ 0 dt a(t) < ∞. Examples are included to illustrate the results. AMS Subject Classification: 34K11, 34K99

By means of some Picone-type identity, we provide some simple oscillation criteria for the equations { a(t)φα(y ′) }′ + q(t)φβ(h(y)) = 0, t > 0; α, β > 0. Mathematics Subject Classification: 34C10, 34K15