Nodal properties of radial solutions for a class of polyharmonic equations

Monica Lazzo; Paul G. Schmidt

doi:10.3934/proc.2007.2007.634

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2007, Volume 2007: 634-643. Doi: 10.3934/proc.2007.2007.634 open access

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Nodal properties of radial solutions for a class of polyharmonic equations

Monica Lazzo^1, and
Paul G. Schmidt^2,

1.
Dipartimento di Matematica, Università di Bari, via Orabona 4, 70125 Bari
2.
Department of Mathematics and Statistics, Parker Hall, Auburn University, AL 36849-5310

Received: August 31, 2006

Revised: May 31, 2007

Published: August 2007

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Abstract

This paper is concerned with the equation $\Delta^(m)u = f(|x|, u)$, where $\Delta$ is the Laplace operator in $\mathbb{R}^N, N \in \mathbb{N}, m \in \mathbb{N}, and f \in C^(0,1 - )(\mathbb{R}_+ \times \mathbb{R}, \mathbb{R})$. Specifically, we analyze the nodal properties of radial solutions on a ball, under Dirichlet or Navier boundary conditions. We obtain precise information about the number of sign changes and the nature of the zeros of the solutions and their iterated Laplacians.

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Mathematics Subject Classification: Primary: 35B05, 35J40. Secondary: 35J60.

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