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

We study the semilinear elliptic system $$\mathrm{\Delta }u=p(\mathrm{\mid }x\mathrm{\mid })g(v),\mathrm{\Delta }v=q(\mathrm{\mid }x\mathrm{\mid })f(u),x\in {\mathbb{R}}^n,n\ge 3,$$ 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.