Abstract
We are dealing with the problem
−Δu(x)=λh(x)u(x)+g(x)u
p(x)
for
x∈
R
N,
u∈
D
1,2(
R
N),
u⩾0,
where
λ is a real parameter,
N>2,
h and
g are a changing sign functions, and
1<p<
N+2
N−2
. Under suitable assumptions, and by combining the global bifurcation result of Rabinowitz [J. Funct. Anal. 7 (1971) 485–513], with a priori estimates of positive solutions, we prove the existence of a continuum of positive solutions, bifurcating from
λ
1,
h
and −
λ
1,−
h
, the two principal eigenvalues of multiplicity one, of the associated linear problem.