Positive solutions for a system of fourth-order \(p\)-Laplacian boundary value problems
Summary: We investigate the existence of positive solutions for the system of fourth-order \(p\)-Laplacian boundary value problems \[ (|u''|^{p-1} u'')''= f_1(t,u,v),\;(|v''|^{q-1} v'')''= f_2(t,u,v), \] \[ u^{(2i)}(0)= u^{(2i)}(1)= 0,\;i=0,1,\;v^{(2i)}(0)= v^{(2i)}(1)= 0,\;i= 0,1, \] where \(p,q> 0\) and \(f_1,f_2\in C([0,1]\times \mathbb{R}^2_+ \mathbb{R}_+)\) \((\mathbb{R}_+:= [0,\infty))\). Based on a priori estimates achieved by using Jensen's integral inequalities and nonnegative matrices, we use fixed point theory to establish our main results.
scientific article; zbMATH DE number 6356632
scientific article