Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations

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Date

2011

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Pergamon-elsevier Science Ltd

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

New oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the form (r(t)Phi(alpha)(x'))' + q(t)(Phi)(x) + Sigma(n)(k=1)q(k)(t)Phi beta(k)(x ) = e(t), t not equal theta(I) x(theta(+)(i)) = ajx(theta(+)(i)) = b(i)x'(theta(i)) where Phi(gamma):= ,s vertical bar(gamma-1)s and beta(1) > beta(2) > ... > beta(m) > alpha > beta(m+1)> ... > beta(n) > beta(n) > 0. If alpha = 1 and the impulses are dropped, then the results obtained by Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] are recovered. Examples are given to illustrate the results. (C) 2011 Elsevier Ltd. All rights reserved.

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Zafer, Agacik/0000-0001-8446-1223; Ozbekler, Abdullah/0000-0001-5196-4078

Keywords

Forced equation, Mixed nonlinear, Interval criteria, Oscillation, Impulse

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Citation

27

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Volume

61

Issue

4

Start Page

933

End Page

940

URI

https://doi.org/10.1016/j.camwa.2010.12.041
 https://hdl.handle.net/20.500.14411/1566

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