Positive Solutions and Nonlinear Multipoint Conjugate Eigenvalue Problems

Abstract

Values of λ are determined for which there exist solutions in a cone of the nth order nonlinear differential equation, u(n) = λa(t)f(u), 0 <t< 1, satisfying the multipoint boundary conditions, u(j)(ai) = 0, 0 ≤ j ≤ ni−1, 1 ≤ i ≤ k, where 0 =a1 < a2 < ... <ak = 1, and Σk i=1 ni = n, where a and f are nonnegative valued, and where both lim f(x) / |x| and lim f(x)/|x| |x|→∞ exist. |x|