Curves of Positive Solutions for Supercritical Problems

For the Dirichlet problem on ball in R n with p < ( n + s )/( n m 2), we show existence of a critical u 0 > 0, such that there are two positive radial solutions for u ] (0, u 0 ), one at u = u 0 , and none for u > u 0 . In another direction we show that for the model problem with 1 h q < ( n + 2)/( n m 2) < p , on a bounded star-shaped domain in R n , there is a u * > 0 so that the problem has no positive solution for u < u *.

Keywords:

• Multiplicity Of Solutions
• Non-existence For Supercritical Problems