Electron. J. Diff. Eqns., Vol. 2004(2004), No. 11, pp. 1-17.

Riccati-type inequality and oscillation criteria for a half-linear PDE with damping

Robert Marik

Under suitable conditions on the coefficients of a partial differential equation, we prove a Riccati-type inequality. As an application of this result, we find oscillation criteria for second order damped half-linear partial differential equations. These criteria improve and complement earlier results on oscillation for partial differential equations. The main feature in our results is that the oscillation criteria are not radially symmetric and do not depend only on the mean value of the coefficients. We consider unbounded domains and state a special oscillation criterion for conic domains.

Submitted October 10, 2003. Published January 15, 2004.
Math Subject Classifications: 35J60, 35B05.
Key Words: p-Lapalacian, oscillatory solution, Riccati equation, half-linear equation, damped equation, differential equation.

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Robert Marik
Dept. of Mathematics, Mendel University
Zemedelska 3
613 00 Brno, Czech Republic
e-mail: marik@mendelu.cz
phone: +420 545 134 030

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