Não disponível

Consider the two-point boundary value problem (1; λ, μ) x" + g ( t, x, x,', λ, μ) = 0 Mx(0) + Nx(b) = K where x = (x, x')^t; M, N are 2x2 matrices such that the rank (M, N) = 2; K = (K₁, K₂)^t is constant; λ μ are real parameters and g is a sufficiently smooth function of its five variables. If x₀ = x₀(t) is a solution of (1; 0,0), we study the local bifurcation of solutions of (1, λ, μ) near x₀. There is a special emphasis on the case where g(t, x, x', 0, 0) = g (x, x') is autonomous under b-periodic boundary conditions, i.e., M = -N = I, K = 0. The case g(t, x, x', λ μ) =g(x, x') + λf₁(t) + λf₂ (t), with f_j(t+b) = f_j(t), j = 1, 2 is studied together with similar versions which include a forced Lotka-Volterra predator-prev model for two species.