Existence of solutions of semilinear systems with gradient dependence via eigenvalue criteria

Abstract

In this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient. These criteria are determined by some relationships between the upper and lower bounds on suitable stripes of $\mathbb R^n$ of the nonlinearities of the system and the principal characteristic values of some associated linear Hammerstein integral operators. Moreover, using smoothing tools, the totality of the involved cone is established.