Oscillation Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities

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2009

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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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Citation Formats

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.