Ordinary differential equations in the oscillation theory of partial half-linear differential equation

In the paper we study the damped half-linear partial differential equation div ( A ( x ) ‖ ∇ u ‖ p − 2 ∇ u ) + 〈 b → ( x ) , ‖ ∇ u ‖ p − 2 ∇ u 〉 + c ( x ) | u | p − 2 u = 0 . Using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equa...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-02, Vol.338 (1), p.194-208
Main Author: MARIK, Robert
Format: Article
Language:English
Subjects:
Damped equation
Differential equation
Elliptic equation
Exact sciences and technology
Half-linear equation
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Oscillation
p-Laplacian
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Second-order
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Summary:In the paper we study the damped half-linear partial differential equation div ( A ( x ) ‖ ∇ u ‖ p − 2 ∇ u ) + 〈 b → ( x ) , ‖ ∇ u ‖ p − 2 ∇ u 〉 + c ( x ) | u | p − 2 u = 0 . Using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equation from oscillation criteria for ordinary differential equations. Using careful radialization we improve several known oscillation criteria.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.05.015