On an indefinite semilinear elliptic problem on RN

We are dealing with the problem [GRAPHICS] where lambda 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 lambda(1,h) and -lambda(1,-h), the two principal eigenvalues of multiplicity one, of the associated linear problem. (C) 2004 Elsevier Inc. All rights reserved.