Positive solutions for a system of second-order quasilinear boundary value problems. (June 2020) - Yang, Zhilin; Wang, Xiaomei; Li, Hongyu
Abstract: In this paper we study the existence and multiplicity of positive solutions for the system of second-order quasilinear boundary value problems − ( ( u ′ ) p − 1 ) ′ = f ( t, u, v ), − ( ( v ′ ) q − 1 ) ′ = g ( t, u, v ), u ( 0 ) = u ′ ( 1 ) = 0, v ( 0 ) = v ′ ( 1 ) = 0, where p, q > 1 and f, g ∈ C ( [ 0, 1 ] × R + 2, R + ) ( R + ≔ [ 0, ∞ ) ) . Based on a priori estimates achieved by utilizing Jensen's inequality for nonnegative concave functions and homogeneous operators, we use fixed point index theory to establish the main results.