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Nodal properties of radial solutions for a class of polyharmonic equations

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


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