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Existence of sign changing solutions for an equation with a weighted p-Laplace operator

Manásevich, Raul; Garcia-Huidobro, Marta; Dolbeault, Jean; Cortázar, Carmen (2014), Existence of sign changing solutions for an equation with a weighted p-Laplace operator, Nonlinear Analysis: Theory, Methods & Applications, 110, p. 1-22. http://dx.doi.org/10.1016/j.na.2014.07.016

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00985507
Date
2014
Journal name
Nonlinear Analysis: Theory, Methods & Applications
Volume
110
Publisher
Elsevier
Pages
1-22
Publication identifier
http://dx.doi.org/10.1016/j.na.2014.07.016
Metadata
Show full item record
Author(s)
Manásevich, Raul
Garcia-Huidobro, Marta
Dolbeault, Jean cc
Cortázar, Carmen
Abstract (EN)
We consider radial solutions of a general elliptic equation involving a weighted $p$-Laplace operator with a subcritical nonlinearity. By a shooting method we prove the existence of solutions with any prescribed number of nodes. The method is based on a change of variables in the phase plane, a very general computation of an angular velocity and new estimates for the decay of an energy associated with an asymptotic Hamiltonian problem. Estimating the rate of decay for the energy requires a sub-criticality condition. The method covers the case of solutions which are not compactly supported or which have compact support. In the last case, we show that the size of the support increases with the number of nodes.
Subjects / Keywords
Energy methods; Hamiltonian systems; Double zero; Compact support principle; Shooting method; Nodes; Nodal solutions; p-Laplace operator

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