First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs
The authors report results on the first variation of the principle eigenvalue for a nonlinear eigenvalue problem associated to a sublinear elliptic boundary value problem stemming from holomorphic perturbations of the boundary. This analysis is used to establish the pointwise 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.
sublinear elliptic boundary value problem
holomorphic perturbations of the boundary
scientific article; zbMATH DE number 1212355
scientific article