On Positive Solutions For Systems Of Nonlinear Sturm-Liouville Differential Equations

This paper is devoted to dealing with the existence of component-wise positive solutions and multiplicity of positive solutions for systems of nonlinear Sturm-Liouville differential equations.In the case of existence of component-wise positive solutions,one nonlinear term is uniformly superlinear or uniformly sublinear,and the other is locally uniformly superlinear or locally uniformly sublinear.In the case of multiplicity of positive solutions,we introduce the notion of a strict lower/upper solution to systems of nonlinear Sturm-Liouville differential equations,based on the maximum principles,we establish a result of Leray-Schauder degree on the ordered intervals induced by the pairs of strict lower and upper solutions.Applying the product formula of fixed point index on product cone,fixed point index theory in cone and the result on Leray-Schauder degree,we obtain our main results.As applications,we consider the existence of component-wise positive solutions for systems of second-order ordinary differential equations with Dirichlet boundary value conditions and Sturm-Liouville nonlinear eigenvalue problem.