Infinitely many radial solutions for a $ p $-Laplacian problem with indefinite weight

Alfonso Castro; Jorge Cossio; Sigifredo Herrón; Carlos Vélez

doi:10.3934/dcds.2021058

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2021, Volume 41, Issue 10: 4805-4821. Doi: 10.3934/dcds.2021058

This issue Previous Article On the mixing and Bernoulli properties for geodesic flows on rank 1 manifolds without focal points Next Article An approximation of forward self-similar solutions to the 3D Navier-Stokes system

Infinitely many radial solutions for a $ p $-Laplacian problem with indefinite weight

1.
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
2.
Escuela de Matemáticas, Universidad Nacional de Colombia, Apartado Aéreo 3840, Medellín, Colombia

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

Received: September 2020

Revised: February 2021

Early access: March 2021

Published: October 2021

The last two authors are supported by Facultad de Ciencias, Universidad Nacional de Colombia sede Medellín

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Abstract

We prove the existence of infinitely many sign changing radial solutions for a $ p $-Laplacian Dirichlet problem in a ball. Our problem involves a weight function that is positive at the center of the unit ball and negative in its boundary. Standard initial value problems-phase plane analysis arguments do not apply here because solutions to the corresponding initial value problem may blow up near the boundary due to the fact that our weight function is negative at the boundary. We overcome this difficulty by connecting the solutions to a singular initial value problem with those of a regular initial value problem that vanishes at the boundary.

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Mathematics Subject Classification: Primary: 35J92, 34B15; Secondary: 34G20.

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References

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