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

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Jorge Cossio, Universidad Nacional de Colombia
Sigifredo Herrón, Universidad Nacional de Colombia
Carlos Vélez, Universidad Nacional de Colombia

Document Type

Article

Department

Mathematics (HMC)

Publication Date

10-2021

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.

Comments

Authors' post-print manuscript available for download.

For the publisher's PDF, please visit https://www.aimsciences.org/article/doi/10.3934/dcds.2021058.

Rights Information

© 2021 American Institute of Mathematical Sciences

Terms of Use & License Information

This work is licensed under a Creative Commons Attribution 4.0 License.

DOI

10.3934/dcds.2021058

Recommended Citation

Alfonso Castro, Jorge Cossio, Sigifredo Herrón, Carlos Vélez. Infinitely many radial solutions for a -Laplacian problem with indefinite weight. Discrete and Continuous Dynamical Systems, 2021, 41(10): 4805-4821.