Existence of Nonnegative Solutions of Linear Autonomous Functional Differential Equations

Abstract

It is shown that if we exclude the existence of nontrivial small solutions, then a linear autonomous functional differential equation has a nontrivial nonnegative solution if and only if it has a nonnegative eigenfunction.

Keywords

• linear functional differential equation
• nonnegative solution
• small solution
• characteristic equation
• eigenfunction
• decomposition theory