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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00985507
Journal nameNonlinear Analysis: Theory, Methods & Applications
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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 / KeywordsEnergy methods; Hamiltonian systems; Double zero; Compact support principle; Shooting method; Nodes; Nodal solutions; p-Laplace operator
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