## All HMC Faculty Publications and Research

Article

#### Department

Mathematics (HMC)

7-1989

#### Abstract

We consider the existence of radially symmetric non-negative solutions for the boundary value problem

\begin{displaymath}\begin{array}{*{20}{c}} { - \Delta u(x) = \lambda f(u(x))\qua... ...\\ {u(x) = 0\quad \left\Vert x \right\Vert = 1} \\ \end{array} \end{displaymath}

where $\lambda > 0,f(0) < 0$ (non-positone), $f' \geq 0$ and $f$ is superlinear. We establish existence of non-negative solutions for $\lambda$ small which extends some work of our previous paper on non-positone problems, where we considered the case $N = 1$. Our work also proves a recent conjecture by Joel Smoller and Arthur Wasserman.

[Note: Abstract cotains a large amount of math type. It is preserved here in its original LaTeX form]

First published in Proceedings of the American Mathematical Society in Vol 106-3(1989), published by the American Mathematical Society

#### Rights Information

© 1989 American Mathematical Society

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