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Full-Text Articles in Physical Sciences and Mathematics
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Turkish Journal of Mathematics
Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations with a superlinear neutral term to be either oscillatory or convergent to zero asymptotically. Examples illustrating the results are included and some suggestions for further research are indicated.
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Turkish Journal of Mathematics
In this paper the second-order difference equations of the form \[ \Delta^2 x_n=a_nf(n,x_{\sigma(n)})+b_n \] are considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. In particular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study the asymptotic behavior of solutions.