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Nonnegative solutions for a class of radially symmetric nonpositone problems

Authors: Alfonso Castro and R. Shivaji
Journal: Proc. Amer. Math. Soc. 106 (1989), 735-740
MSC: Primary 35B05; Secondary 35J65
MathSciNet review: 949875
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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.

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Keywords: Non-negative solution, non-positone problem, singular o.d.e., Dirichlet problem
Article copyright: © Copyright 1989 American Mathematical Society

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