Bifurcation problems for second order systems.

In this paper, we consider the following linear system of second order differential equations (0.1) u ′ ′ + A (t) u = 0 , 0 ≤ t < ∞ where, for each t , A (t) is an n × n matrix with real components, and positive with respect to the usual cone K in R n. Conditions are provided in order that the first conjugate point T of t = 0 , i.e. the smallest T such that the above equation has a nontrivial solution u : 0 , T → K satisfying the boundary conditions u (0) = 0 = u (T) will be a bifurcation point for higher order perturbations of the equation. The paper is mainly motivated by results in Ahmad and Lazer (1997, 1980); Ahmad and Salazar (1981) and Schmitt (1975); Schmitt and Smith (1978). Some additional new consequences are discussed. [ABSTRACT FROM AUTHOR]