#### Document Type

Article

#### Department

Mathematics (HMC)

#### Publication Date

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.

#### Rights Information

© 1989 American Mathematical Society

#### DOI

10.1090/S0002-9939-1989-0949875-3

#### Recommended Citation

Castro, Alfonso and Shivaji, Ratnasingham, "Nonnegative Solutions for a Class of Radially Symmetric Nonpositone Problems" (1989). *All HMC Faculty Publications and Research*. 461.

https://scholarship.claremont.edu/hmc_fac_pub/461

## Comments

[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