publication . Article . 2006

Oscillation criteria for first-order forced nonlinear difference equations

Agarwal, Ravi P.; Grace, Said R.; Smith, Tim;
Open Access English
  • Published: 01 Jan 2006 Journal: Advances in Difference Equations, volume 2,006, pages 1-17 (issn: 1687-1839, eissn: 1687-1847, Copyright policy)
  • Publisher: SpringerOpen
Abstract
<p/> <p>Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form &#916;<it>x</it>(<it>n</it>)+<it>q</it><sub>1</sub>(<it>n</it>)<it>x</it><sup><it>&#956;</it></sup>(<it>n</it>+1) = <it>q</it><sub>2</sub>(<it>n</it>)<it>x</it><sup><it>&#955;</it></sup>(<it>n</it>+1)+<it>e</it>(<it>n</it>), where <it>&#955;</it>, <it>&#956;</it> are the ratios of positive odd integers 0 &lt;<it>&#956;</it> &lt; 1 and <it>&#955;</it> &gt; 1, are established.</p>
Subjects
free text keywords: Applied Mathematics, Mathematics, Algebra and Number Theory, Analysis, QA1-939

[1] R. P. Agarwal, M. Bohner, S. R. Grace, and D. O'Regan, Discrete Oscillation Theory, Hindawi, New York, 2005.

[2] R. P. Agarwal and S. R. Grace, Forced oscillation of nth-order nonlinear differential equations, Applied Mathematics Letters 13 (2000), no. 7, 53-57.

[3] R. P. Agarwal, S. R. Grace, and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic, Dordrecht, 2000.

[4] R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, Mathematics and Its Applications, vol. 404, Kluwer Academic, Dordrecht, 1997.

[5] M. Cecchi, Z. Dosˇla´, and M. Marini, Nonoscillatory half-linear difference equations and recessive solutions, Advances in Difference Equations 2005 (2005), no. 2, 193-204.

[6] G. H. Hardy, J. E. Littlewood, and G. Po´ lya, Inequalities, 2nd ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988.

Abstract
<p/> <p>Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form &#916;<it>x</it>(<it>n</it>)+<it>q</it><sub>1</sub>(<it>n</it>)<it>x</it><sup><it>&#956;</it></sup>(<it>n</it>+1) = <it>q</it><sub>2</sub>(<it>n</it>)<it>x</it><sup><it>&#955;</it></sup>(<it>n</it>+1)+<it>e</it>(<it>n</it>), where <it>&#955;</it>, <it>&#956;</it> are the ratios of positive odd integers 0 &lt;<it>&#956;</it> &lt; 1 and <it>&#955;</it> &gt; 1, are established.</p>
Subjects
free text keywords: Applied Mathematics, Mathematics, Algebra and Number Theory, Analysis, QA1-939

[1] R. P. Agarwal, M. Bohner, S. R. Grace, and D. O'Regan, Discrete Oscillation Theory, Hindawi, New York, 2005.

[2] R. P. Agarwal and S. R. Grace, Forced oscillation of nth-order nonlinear differential equations, Applied Mathematics Letters 13 (2000), no. 7, 53-57.

[3] R. P. Agarwal, S. R. Grace, and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic, Dordrecht, 2000.

[4] R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, Mathematics and Its Applications, vol. 404, Kluwer Academic, Dordrecht, 1997.

[5] M. Cecchi, Z. Dosˇla´, and M. Marini, Nonoscillatory half-linear difference equations and recessive solutions, Advances in Difference Equations 2005 (2005), no. 2, 193-204.

[6] G. H. Hardy, J. E. Littlewood, and G. Po´ lya, Inequalities, 2nd ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988.

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publication . Article . 2006

Oscillation criteria for first-order forced nonlinear difference equations

Agarwal, Ravi P.; Grace, Said R.; Smith, Tim;