Qualitative Properties and Existence of Sign Changing Solutions with Compact Support for an Equation with a p-Laplace Operator

We consider radial solutions of an elliptic equation involving the p-Laplace operator and prove by a shooting method the existence of compactly supported solutions with any prescribed number of nodes. The method is based on a change of variables in the phase plane corresponding to an asymptotic Hami...

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Bibliographic Details
Published in:Advanced nonlinear studies 2013-02, Vol.13 (1), p.149-178
Main Authors: Dolbeault, Jean, García-Huidobro, Marta, Manasevich, Raul
Format: Article
Language:English
Subjects:
Compact support principle
Energy methods
Hamiltonian systems
Nodal solutions
Nodes
p-Laplace operator
Shooting method
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Summary:We consider radial solutions of an elliptic equation involving the p-Laplace operator and prove by a shooting method the existence of compactly supported solutions with any prescribed number of nodes. The method is based on a change of variables in the phase plane corresponding to an asymptotic Hamiltonian system and provides qualitative properties of the solutions.
ISSN:1536-1365
2169-0375
DOI:10.1515/ans-2013-0109