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

被引：0

作者：

Cortázar, Carmen ^{[1
]}

Dolbeault, Jean ^{[2
]}

García-Huidobro, Marta ^{[1
]}

Manásevich, Rául ^{[3
]}

机构：

[1] Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306 Correo 22, Santiago, Chile

[2] Ceremade (UMR CNRS No. 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, Paris Cédex 16,75775, France

[3] DIM and CMM (UMR CNRS No. 2071), FCFM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile

来源：

Nonlinear Analysis, Theory, Methods and Applications | 2014年 / 110卷

关键词：

Control nonlinearities - Laplace transforms;

D O I：

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学科分类号：

摘要：

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. © 2014 Elsevier Ltd.

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