Existence and large radial solutions for an elliptic system under finite new Keller-Osserman integral conditions

Abstract

We study the semilinear elliptic system \[ \Delta u = p(|x|)\,g(v), \qquad \Delta v = q(|x|)\,f(u), \qquad x \in \mathbb{R}^n,\; n \geq 3, \] under new Keller--Osserman-type integral conditions on the nonlinearities $f,g$ and decay constraints on the radial weights $p,q$. Within this framework we prove: (i) existence of infinitely many entire positive radial solutions for admissible central values; (ii) closedness of the set of all admissible central values; and (iii) largeness (blow-up at infinity) of solutions at boundary points. The analysis combines comparison principles, compactness arguments, and Keller--Osserman transforms, thereby extending classical theory to coupled elliptic systems with general nonlinearities and weights.