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Oscillation Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities
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938706.pdf
Date
2009
Author
Agarwal, Ravi P.
Zafer, A.
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We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (r(t)Phi(alpha)(x(Delta)))(Delta) + f(t,x(sigma)) = e(t), t is an element of [t(0), infinity)(T) with f (t, x) = q(t) Phi(alpha)(x) + Sigma(n)(i=1)q(i)(t)Phi(beta i)(x), Phi(*)(u) = vertical bar u vertical bar*(-1) u, where [t(0), infinity)(T) is a time scale interval with t(0) is an element of T, the functions r, q, q(i), e : [t(0), infinity)(T) -> R are right-dense continuous with r > 0, sigma is the forward jump operator, x(sigma) (t) := x(sigma(t)), and beta(1) > ... > beta(m) > alpha > beta(m+1) > ... beta(n) > 0. All results obtained are new even for T = R and T = Z. In the special case when T = R and alpha = 1 our theorems reduce to (Y. G. Sun and J. S. W. Wong, Journal of Mathematical Analysis and Applications. 337 (2007), 549-560). Therefore, our results in particular extend most of the related existing literature from the continuous case to arbitrary time scale. Copyright (C) 2009 R. P. Agarwal and A. Zafer.
Subject Keywords
Algebra and Number Theory
,
Applied Mathematics
,
Analysis
URI
https://hdl.handle.net/11511/50951
Journal
Advances in Difference Equations
DOI
https://doi.org/10.1155/2009/938706
Collections
Department of Mathematics, Article
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R. P. Agarwal and A. Zafer, “Oscillation Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities,”
Advances in Difference Equations
, pp. 1–20, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/50951.