Positive solutions for systems of nonlinear eigenvalue problems for functional differential equations

Abstract

Values of λ are determined for which there exist positive solutions of the system of functional differential equations, u″ + λa(t)f(v _t ) = 0,v″ + λb(t)g(u _t ) = 0, for 0 < t < 1, satisfying the initial conditions u(s) = v(s) = φ(s), −r ≤ s ≤ 0, and the boundary conditions u(0) = v(0) = φ(0) = u(1) = v(1) = 0. A Guo–Krasnosel'skii fixed point theorem is applied.

Keywords:

• System of functional differential equations
• Boundary value problem
• Eigenvalue problem

Keywords:

• AMS (MOS) Subject Classifications:
• 34K10
• 34A34