We study the existence of positive radial solutions to the problem 8 { -Δpu = λK1(jxj)f(v) in Ωe; -Δpv = λK2(jxj)g(u) in Ωe; u = v = 0 if jxj = r0; u(x) → 0; v(x) → 0 as jxj → 1; where Δpw := div(jrwjp-2rw), 1 < p < n, λ is a positive parameter, r0 > 0 and Ωe := {x 2 Rnj jxj > r0}. Here, Ki : [r0;∞) → (0;∞), i = 1; 2 are continuous functions such that limr→1 Ki(r) = 0, and f; g : [0;1) → R are continuous functions which are negative at the origin and have a superlinear growth at infinity. We establish the existence of a positive radial solution for small values of λ via degree theory and rescaling arguments. © 2018 Khayyam Publishing. All rights reserved.}, funding_details={Simons FoundationSimons Foundation, 317872}, funding_details={European Social FundEuropean Social Fund, ESF}, funding_text_1={Since ‖u‖∞ → ∞ as λ → 0, we have maxt∈[0,1]f(v(t)) → ∞ as λ → 0. This implies that ‖v‖∞ → ∞ as λ → 0. Similarly if ‖v‖∞ → ∞ as λ → 0, we can prove ‖u‖∞ → ∞ as λ → 0. Hence, both ‖u‖∞ and ‖v‖∞ → ∞ as λ → 0. Hence, Theorem 1.1 is proven. Acknowledgment. This work was partially supported by the project EXLIZ-CZ.1.07/2.3.00/30.0013, which is co-financed by the European Social Fund and the state budget of the Czech Republic and by the INSPIRE faculty award by the Department of Science and Technology, India for Lakshmi Sankar. 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Equ.}, document_type={Article}, source={Scopus},