First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs

In this paper the first variation of the principal eigenvalue of -Delta in Omega(0), with respect to a general family of holomorphic perturbations of Omega(0), is analyzed. Then, the results from this analysis are used to ascertain the point-wise growth to infinity of the positive solutions of a class of sublinear elliptic boundary value problems with vanishing coefficients at the value of the parameter where bifurcation from infinity occurs. (C) 1998 Academic Press.