Homoclinics for an Almost Periodically Forced Singular Hamiltonian System
نویسندگان
چکیده
where a and W satisfy (a1) a(t) is a continuous almost periodic function of t with a(t) ≥ a0 > 0 for all t ∈ R. (W1) There is a ξ ∈ R\{0} such that W ∈ C(R\{ξ},R). (W2) limx→ξW (x) = −∞. (W3) There is a neighborhood N of ξ and U ∈ C(N\{ξ},R) such that |U(x)| → ∞ as x→ ξ and |U ′(x)|2 ≤ −W (x) for x ∈ N\{ξ}, (W4) W (x) < W (0) = 0 if x 6= 0 and W ′′(0) is negative definite. (W5) There is a constant W0 < 0 such that limx→∞W (x) ≤W0. When a is periodic in t and somewhat weaker conditions than (a1) and (W1)–(W5) are satisfied, it was shown in [17] that (HS) possesses a pair of solutions that are homoclinic to 0 and wind around ξ in a positive and negative sense
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