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Riccati inequality and oscillation criteria for PDE with
-Laplacian
Journal of Inequalities and Applications volume 2006, Article number: 63061 (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.
References
- 1.
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.
- 2.
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.1998.6159
- 3.
Philos ChG: Oscillation theorems for linear differential equations of second order. Archiv der Mathematik. Archives of Mathematics. Archives Mathématiques 1989,53(5):482–492.
- 4.
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/BF01783687
- 5.
Wintner A: A criterion of oscillatory stability. Quarterly of Applied Mathematics 1949, 7: 115–117.
- 6.
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.2000.7376
- 7.
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)00270-4
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Xu, Z. Riccati inequality and oscillation criteria for PDE with-Laplacian.
J Inequal Appl 2006, 63061 (2006). https://doi.org/10.1155/JIA/2006/63061
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Keywords
- Oscillation Criterion
- Riccati Inequality