]>
2011
4
3
ISSN 2008-1898
37
Oscillation of second-order quasi-linear neutral functional dynamic equations with distributed deviating arguments
Oscillation of second-order quasi-linear neutral functional dynamic equations with distributed deviating arguments
en
en
In this paper, some sufficient conditions for the oscillation of
second-order nonlinear neutral functional dynamic equation
\[( r(t) ( [x(t) + p(t)x[\tau (t)]]^\Delta)^\gamma )^\Delta +\int^b_a q(t; \xi)x^\gamma [g(t; \xi)]\Delta\xi= 0; t \in \mathbb{T}\]
are established. An example is given to illustrate an application of our results.
180
192
Tongxing
Li
School of Control Science and Engineering
School of mathematical Sciences
Shandong University
University of Jinan
P. R. China
P. R. China
litongx2007@163.com
Ethiraju
Thandapani
Ramanujan Institute for Advanced Study in Mathematics
University of Madras
India
ethandapani@yahoo.co.in
Oscillation
Second-order nonlinear equation
Neutral dynamic equation
Distributed deviating arguments
Time scale.
Article.1.pdf
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R. P. Agarwal, M. Bohner, D. O’Regan, A. Peterson, Dynamic equations on time scales: a survey, J. Comput. Appl. Math., 141 (2002), 1-26
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R. P. Agarwal, D. O’Regan, S. H. Saker, Oscillation criteria for second-order nonlinear neutral delay dynamic equations, J. Math. Anal. Appl., 300 (2004), 203-217
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R. P. Agarwal, D. O’Regan, S. H. Saker , Philos-type oscillation criteria of second-order half-linear dynamic equations on time scales, Rocky Mount. J. Math., 37 (2007), 1085-1104
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M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston (2001)
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M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston (2003)
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D. X. Chen, Oscillation of second-order Emden–Fowler neutral delay dynamic equations on time scales, Math. Comput. Modelling, 51 (2010), 1221-1229
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D. X. Chen, J. C. Liu, Asymptotic behavior and oscillation of solutions of third-order nonlinear neutral delay dynamic equations on time scales, Can. Appl. Math. Q., 16 (2008), 19-43
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L. Erbe, A. Peterson, S. H. Saker, Oscillation criteria for second-order nonlinear delay dynamic equations, J. Math. Anal. Appl., 333 (2007), 505-522
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L. Erbe, T. S. Hassan, A. Peterson, Oscillation criteria for nonlinear damped dynamic equations on time scales, Appl. Math. Comput, 203 (2008), 343-357
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Z. Han, T. Li, S. Sun, C. Zhang, On the oscillation of second-order neutral delay dynamic equations on time scales, Afri. Dia. J. Math., 9 (2010), 76-86
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S. H. Saker, D. O’Regan, New oscillation criteria for second-order neutral functional dynamic equations via the generalized Riccati substitution, Commun. Nonlinear Sci. Numer. Simulat, 16 (2011), 423-434
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S. H. Saker, D. O’Regan, New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati technique, Hirosh. math. J., 41 (2011), 1-22
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S. H. Saker, D. O’Regan, R. P. Agarwal, Oscillation theorems for second-order nonlinear neutral delay dynamic equations on time scales, Acta. Math. Sinica, 24 (2008), 1409-1432
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]
Internal nonlocal and integral condition problems of the differential equation \(x' = f(t; x; x')\)
Internal nonlocal and integral condition problems of the differential equation \(x' = f(t; x; x')\)
en
en
In this work, we are concerned with the existence of at least
one absolutely continuous solution of the Cauchy problem for the differential
equation \(x' = f(t; x; x'), t \in (0; 1)\) with the internal nonlocal condition m
\(\sum^m_{k=1} a_kx(\tau_k) = x_o, \tau_k \in (c, d) \subseteq (0; 1)\). The problem of the integral
condition
\(\int^d_c x(s) dg(s) = x_o\) will be considered.
193
199
A. M. A.
El-Sayed
Department of Mathematics
Alexandria University
Egypt
amasayed@hotmail.com
E. M.
Hamdallah
Department of Mathematics
Alexandria University
Egypt
emanhamdalla@hotmail.com
KH. W.
Elkadeky
Department of Mathematics, Faculty of Science
Garyounis University
Libya
k-welkadeky@yahoo.com
Nonlocal conditions
integral condition
existence of solution
fixedpoint theorem
Article.2.pdf
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]
Existential Results for Nonlinear Singular Interface Problems involving Second Order Nonlinear Dynamic Equations using Picards Iterative Technique
Existential Results for Nonlinear Singular Interface Problems involving Second Order Nonlinear Dynamic Equations using Picards Iterative Technique
en
en
In this paper we give existential results for nonlinear interface
problems with a singular interface. The solution is proved to exist for an IVP
satisfying matching interface conditions. The picards iterative technique is
used. We discuss the theory developed to a problem in the field of applied
elasticity.
200
209
D. K. K.
Vamsi
Department of Mathematics and Computer Science
Sri Sathya Sai Institute of Higher Learning
India
dkkvamsi,baruahpk@sssu.edu.in
PALLAV KUMAR
BARUAH
Department of Mathematics and Computer Science
Sri Sathya Sai Institute of Higher Learning
India
regular problems
singular problems
singular interface problems
picards iterative technique
Article.3.pdf
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##[2]
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Pallav Kumar Baruah, M. Venkatesulu, Deficiency indices of a differential operator satisfying certain matching interface conditions, Electron. J. Differential Equations , 38 (2005), 1-9
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Pallav Kumar Baruah, M. Venkatesulu, Number of linearly independent square integrable solutions of a pair of ordinary differential equations satisfying certain matching interface conditions, Int. J. Math. Anal. , 3 (2006), 131-144
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Pallav Kumar Baruah, M. Venkatesulu , Self adjoint boundary value problems associated with a pair of singular ordinary differential expressions with interface spatial conditions, , (to appear), -
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Pallav Kumar Baruah, M. Venkatesulu, Spectrum of pair of ordinary differential operators with a matching interface conditions, Int. Rev. Pure Appl. Math. , 4 (), 39-47
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]
Some fixed point results in ordered partial metric spaces
Some fixed point results in ordered partial metric spaces
en
en
In this paper, we establish some fixed point theorems in ordered
partial metric spaces. An example is given to illustrate our obtained results.
210
217
Hassen
Aydi
Institut Supérieur d'Informatique de Mahdia
Universitéde Monastir
Tunisie
hassen.aydi@isima.rnu.tn
Fixed point
partial metric space
ordered set.
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]