Positive Solutions of Superlinear Elliptic Equations

In this paper, we study the existence of two positive solutions of superlinear elliptic equations without assuming the conditions which have been used in the literature to deduce either the P.S. condition or a priori bounds of positive solutions. The first solution is proved as the minimal positive solution, while the second one is obtained as the limit of a gradient flow whose starting point is properly chosen. The dependence of the minimal solution upon a parameter is also considered.