Entire large positive radial symmetry solutions for combined quasilinear elliptic system

Abstract

We prove the existence of entire large positive solutions to the system    (r N−1φ1(u ′ ))′ = r N−1P1(r)f(u, v), 0 ≤ r < ∞ (r N−1φ2(v ′ ))′ = r N−1P2(r)g(u, v), 0 ≤ r < ∞ u(0) = a, v(0) = b, u′ (0) = 0, v′ (0) = b, where the functions φi(s) = αi(s 2 )s, i = 1, 2 are odd, increasing homeomorphisms, P1, P2 : [0, ∞) → [0, ∞) are continuous, and f, g : [0, ∞) × [0, ∞) → [0, ∞) are continuous and increasing functions.