Electron. J. Diff. Eqns., Vol. 2007(2007), No. 01, pp. 1-7.



On oscillation and asymptotic behaviour of a neutral differential equation of first order with positive and negative coefficients

Radhanath Rath, Prayag Prasad Mishra, Laxmi Narayan Padhy

Abstract:
In this paper sufficient conditions are obtained so that every solution of
$$ (y(t)- p(t)y(t-\tau))'+ Q(t)G(y(t-\sigma))-U(t)G(y(t-\alpha)) = f(t) $$
tends to zero or to $\pm \infty$ as $t$ tends to $\infty$, where $\tau ,\sigma ,\alpha$ are positive real numbers, $p,f\in C([0,\infty),R),Q,U\in C([0,\infty),[0,\infty))$, and $G\in C(R,R)$, $G$ is non decreasing with $xG(x)$ greater than 0 for $ x\neq 0$. The two primary assumptions in this paper are $\int_{t_0}^{\infty}Q(t)=\infty$ and . The results hold when $G$ is linear, super linear,or sublinear and also hold when $f(t) \equiv 0$. This paper generalizes and improves some of the recent results in [5,7,8,10].

Submitted November 2, 2006. Published January 2, 2007
Math Subject Classifications: 34C10, 34C15, 34K40.
Key Words: Oscillatory solution; nonoscillatory solution; asymptotic behaviour.

Show me the DVI(62K), PDF(216K), TEX and other files for this article.

source from : ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (EJDE)

Komentar

Anonim mengatakan…
I just added your website on my blogroll. I may come back later on to check out updates. Excellent information!
8 Agustus 2011 pukul 15.31
Anonim mengatakan…
I just added your website on my blogroll. Really enjoyed reading through. Excellent information!
10 Agustus 2011 pukul 05.38
Anonim mengatakan…
Really great article with very interesting information. You might want to follow up to this topic!?! 2011
21 Agustus 2011 pukul 02.18
Posting Komentar

Postingan populer dari blog ini

Galaxies Are Born Of Violence Between Dark Matter and Interstellar Gas

Gambar
Picture on Left is Dwarf galaxy forming one billion years after the Big Bang. The background image shows the large-scale cosmic context (the panel is approximately 100,000 light years across); the inset shows the central 2,000 light years of the dwarf galaxy where powerful feedback from newly born star clusters drives bulk motions in the gas. Stars are shown in yellow; colours from violet to blue to green to white correspond to gas of increasing density. (Credit: S. Mashchenko, J. Wadsley, and H. M. P. Couchman) ============================================= ScienceDaily (Nov. 30, 2007) — Researchers using supercomputer simulations have exposed a very violent and critical relationship between interstellar gas and dark matter when galaxies are born -- one that has been largely ignored by the current model of how the universe evolved. The findings, published in Science, solve a longstanding problem of the widely accepted model -- Cold Dark Matter cosmology -- which suggests there is muc...
Baca selengkapnya

ntelligent Software Helps Build Perfect Robotic Hand

Gambar
Figure on Left is The 'cyberglove' used to capture data about how the human hand moves. (Credit: Image courtesy of University Of Portsmouth) ScienceDaily (Nov. 30, 2007) — Scientists in Portsmouth and Shanghai are working on intelligent software that will take them a step closer to building the perfect robotic hand. Using artificial intelligence, they are creating software which will learn and copy human hand movements. They hope to replicate this in a robotic device which will be able to perform the dexterous actions only capable today by the human hand. Dr Honghai Liu, senior lecturer at the University of Portsmouth’s Institute of Industrial Research, and Professor Xiangyang Zhu from the Robotics Institute at Jiao Tong University in Shanghai, were awarded a Royal Society grant to further their research. The technology has the potential to revolutionise the manufacturing industry and medicine and scientists hope that in the future it could be used to produce the perfect a...
Baca selengkapnya

Integral Trigonometri

Gambar
Integral Trigonometri merupakan hasil kebalikan dari turunan trigonometri. Sebelum kita mencoba mengingat rumus-rumus integral triogonometri maka sebaiknya kita ingat dulu turunan trigonometri. Turunan trigonometri bisa kita tuliskan sebagai berikut y = sin x maka y' = cos x y = cos x maka y' = - sin x y = tan x maka y' = sec 2 x y = cot x maka y' = -csc 2 x y = sec x maka y' = sec x tan x y = csc x maka y' = -csc x cot x Dengan demikian jika rumus-rumus ini kita balik akan menjadi Rumus-rumus tersebut bisa dibuat lebih umum sebagai berikut Untuk lebih jelasnya kita bisa membuktikan sebagai berikut misalkan : y = ax + b maka Jadi :
Baca selengkapnya