An existence theorem for positive solutions of degenerate semilinear elliptic equations. (English) Zbl 0701.35074
The degenerate semilinear elliptic problem
\[
(*)\quad \Delta (u^ m)+u(1-u)(u-a)=0\text{ in } \Omega,\quad u=0\text{ on } \partial \Omega,
\]
is studied for a ball \(\Omega\) of radius R in \({\mathbb{R}}^ n\). The existence of positive radial solutions of more general equation is studied through the analysis of the associated ordinary differential equation. As a result the existence of positive solutions of (*) with \(0<a<(m+1)/(m+3)\) for sufficiently large R is established.
Reviewer: K.Yoshida
MSC:
35J70 | Degenerate elliptic equations |
35J65 | Nonlinear boundary value problems for linear elliptic equations |