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 −ΔinΩ0with respect to a general family of holomorphic perturbations ofΩ0is 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