Positive Solutions and Extremal Points for Differential Equations

Abstract

Extremal point properties are examined for the boundary value problem x⁽ⁿ⁾ + ? ^n-2 _i=0 A_i(t)x⁽ⁱ⁾ = 0, x⁽ⁱ⁾(0) = x^(n-2)(T) = 0, 0?i?n-2, where the A_i's, a characterization for the first extremal point is given in terms of the existence of a solution which is positive with respect to a cone in a Banach space. Also, an existence theorem is obtained for a related nonlinear problem

Keywords:

• Positive solution
• cone
• boundary value problem
• eigenvalue
• extremal point