Heriot-Watt Mathematics Report Series
HWM98-7, 16 Feb 1998
Positive Solutions for a Semilinear Elliptic Problem with Sign-Changing Nonlinearity
G A Afrouzi and K J Brown
Abstract
By using the implicit function theorem we obtain closely linked
necessary and sufficient conditions for the existence of positive
solutions for the semilinear boundary value problem
$$
- \Delta u = \lambda a(x) f(u) \mbox{ on } \Omega;
\hspace{.2in} u = 0 \mbox{ on }\partial \Omega
$S
for small positive values of the parameter $\lambda$ where $\Omega$ is
a bounded region, the coefficient $a$ changes sign and the
nonlinearity $f$ is such that $f(0) > 0$.
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