New existence theorems of positive solutions for Sturm-Liouville boundary value problems

By constructing available operators some new existence theorems of positive solutions are obtained for the Sturm-Liouville boundary value problem(p(t)u^'(t))^'[email protected](t)f(t,u(t))=0,@a"1u(0)[email protected]"1p(0)u^'(0)=0,@a"2u(1)[email protected]"2p(1)u^'(1)=0,where a(t)>=0 and @l>0 is a parameter.