Nodal properties of radial solutions for a class of polyharmonic equations

Pages: 634 - 643, Issue Special, September 2007

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Monica Lazzo - Dipartimento di Matematica, Università di Bari, via Orabona 4, 70125 Bari, Italy (email)
Paul G. Schmidt - Department of Mathematics and Statistics, Parker Hall, Auburn University, AL 36849-5310, United States (email)

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.

Keywords:  Polyharmonic equations, radial solutions, nodal properties, Dirichlet boundary conditions, Navier boundary conditions.
Mathematics Subject Classification:  Primary: 35B05, 35J40. Secondary: 35J60.

Received: September 2006;      Revised: June 2007;      Published: September 2007.