Riccati inequality and oscillation criteria for PDE with -Laplacian

Zhiting Xu

doi:10.1155/JIA/2006/63061

Journal of Inequalities and Applications Cover Image

Research Article

Open Access

Riccati inequality and oscillation criteria for PDE with -Laplacian

Zhiting Xu¹Email author

Journal of Inequalities and Applications20062006:63061

https://doi.org/10.1155/JIA/2006/63061

Received: 1 November 2003

Accepted: 25 December 2004

Published: 5 March 2006

Abstract

Oscillation criteria for PDE with -Laplacian div are obtained via Riccati inequality. Some of them are extensions of the results for the second-order linear ODE to this equation.

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Authors’ Affiliations

(1)

Department of Mathematics, South China Normal University

References

Díaz JI: Nonlinear Partial Differential Equations and Free Boundaries. Vol. I. Elliptic Equations, Research Notes in Mathematics. Volume 106. Pitman (Advanced Publishing Program), Massachusetts; 1985:vii+323.Google Scholar
Kong Q: Interval criteria for oscillation of second-order linear ordinary differential equations. Journal of Mathematical Analysis and Applications 1999,229(1):258–270. 10.1006/jmaa.1998.6159MATHMathSciNetView ArticleGoogle Scholar
Philos ChG: Oscillation theorems for linear differential equations of second order. Archiv der Mathematik. Archives of Mathematics. Archives Mathématiques 1989,53(5):482–492.MATHMathSciNetView ArticleGoogle Scholar
Usami H: Some oscillation theorems for a class of quasilinear elliptic equations. Annali di Matematica Pura ed Applicata. Series IV 1998, 175: 277–283. 10.1007/BF01783687MATHMathSciNetView ArticleGoogle Scholar
Wintner A: A criterion of oscillatory stability. Quarterly of Applied Mathematics 1949, 7: 115–117.MATHMathSciNetGoogle Scholar
Wong JSW: On Kamenev-type oscillation theorems for second-order differential equations with damping. Journal of Mathematical Analysis and Applications 2001,258(1):244–257. 10.1006/jmaa.2000.7376MATHMathSciNetView ArticleGoogle Scholar
Xu Z-T, Xing H-Y: Oscillation criteria of Kamenev-type for PDE with-Laplacian. Applied Mathematics and Computation 2003,145(2–3):735–745. 10.1016/S0096-3003(03)00270-4MATHMathSciNetView ArticleGoogle Scholar

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