ABSTRACT. It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equationin the space of periodic functions with fixed period w, can be computed in terms of the Brouwer degree of g. This result provides efficient continuation theorems specially for w-periodic perturbations of autonomous systems. Extensions to differential equations in flow-invariant ENR's are also given.

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In this paper we are concerned with a differential equation of the formwhere À14a5b4 þ 1; q has infinitely many zeros in ða; bÞ; and g is superlinear.We prove the existence of solutions with prescribed nodal properties in the intervals of negativity and positivity of q: When c ¼ 0 and q is periodic we show that the equation under consideration exhibits chaotic-like dynamics. # 2002 Elsevier Science (USA)

The existence of 2π-periodic solutions of the second-order differential equationwhere a, b satisfy 1/ √ a + 1/ √ b = 2/n and p(t) = p(t + 2π), t ∈ R, is examined. Assume that limits lim x→±∞ F(x) = F(±∞) (F(x) =

ABSTRACT. It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equationin the space of periodic functions with fixed period w, can be computed in terms of the Brouwer degree of g. This result provides efficient continuation theorems specially for w-periodic perturbations of autonomous systems. Extensions to differential equations in flow-invariant ENR's are also given.