Riccati inequality and oscillation criteria for PDE with -Laplacian
© Zhiting Xu 2006
Received: 1 November 2003
Accepted: 25 December 2004
Published: 5 March 2006
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.
- 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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