Electron. J. Diff. Eqns., Vol. 2004(2004), No. 11, pp. 117.
Riccatitype inequality and oscillation criteria
for a halflinear PDE with damping
Robert Marik
Abstract:
Under suitable conditions on the coefficients of a partial
differential equation, we prove a Riccatitype inequality.
As an application of this result, we find oscillation
criteria for second order damped halflinear 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: pLapalacian, oscillatory solution, Riccati equation,
halflinear equation, damped equation, differential equation.
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Robert Marik
Dept. of Mathematics, Mendel University
Zemedelska 3
613 00 Brno, Czech Republic
email: marik@mendelu.cz
phone: +420 545 134 030 
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