Positive solutions for a system of second-order quasilinear boundary value problems

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.