We prove that the semilinear Dirichlet problem for a Laplace equation on a unit ball, involving the nonlinearity
f(
r,u)=-
a(
r)
u+b(
r)
up, with a subcritical
p, has a unique positive solution, provided
a(
r) is positive, increasing and convex, while
b(
r) is positive, decreasing and concave. Moreover, we prove that this solution is non-degenerate. We also present a uniqueness result in case
a(
r) is negative.
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