Positive Solutions for a System of Fourth-Order p-Laplacian Boundary Value Problems

Abstract

We investigate the existence of positive solutions for the system of fourth-order p-Laplacian boundary value problems (|u′′|p-1u′′)′′=f1(t,u,v),  (|v′′|q-1v′′)′′=f2(t,u,v),  u(2i)(0)=u(2i)(1)=0,  i=0,1,  v(2i)(0)=v(2i)(1)=0,  i=0,1, where p,q>0 and f1,f2∈C([0,1]×ℝ+2,ℝ+)  (ℝ+:=[0,∞)). Based on a priori estimates achieved by utilizing Jensen’s integral inequalities and nonnegative matrices, we use fixed point index theory to establish our main results.