2007, 2007(Special): 634-643. doi: 10.3934/proc.2007.2007.634

Nodal properties of radial solutions for a class of polyharmonic equations

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, United States

Received  September 2006 Revised  June 2007 Published  September 2007

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.
Citation: Monica Lazzo, Paul G. Schmidt. Nodal properties of radial solutions for a class of polyharmonic equations. Conference Publications, 2007, 2007 (Special) : 634-643. doi: 10.3934/proc.2007.2007.634
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