Shooting from singularity to singularity and a quasilinear p-Laplace-Beltrami equation with indefinite weight

Alfonso Castro; Jorge Cossio; Sigifredo Herrón; Carlos Vélez

doi:10.3934/dcdss.2023108

Article Contents

2024, Volume 17, Issue 5&6: 2186-2207. Doi: 10.3934/dcdss.2023108

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Shooting from singularity to singularity and a quasilinear p-Laplace-Beltrami equation with indefinite weight

1.
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
2.
Escuela de Matemáticas, Universidad Nacional de Colombia Sede Medellín, Colombia

^*Corresponding author: Alfonso Castro
^*Corresponding author: Alfonso Castro

Received: November 2022

Revised: April 2023

Early access: May 29, 2023

Published online: May 29, 2023

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Abstract

For surfaces of revolution we prove the existence of infinitely many sign-changing rotationally symmetric solutions to a wide class of $ p $-Laplace-Beltrami equations with polynomial like nonlinearities. We combine the methods in [10] where the semilinear case $ (p = 2) $ with positive weight was studied with those in [5] and [6] where radial solutions to a $ p $-Laplacian Dirichlet problem in a ball was considered. Our equations lead to ordinary differential equations with two singularities and a sign changing weight function which leads to an initial value problem that may blow up in the region of definition of the equation.

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Mathematics Subject Classification: 34A12, 34B16, 34C40, 35A24, 35B07, 35B44, 35J25, 35J92, 58J05.

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References

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