Dynamic Systems and Applications 17 (2008) 637-652 TRIPLE POSITIVE SOLUTIONS OF THREE-POINT BOUNDARY VALUE PROBLEM FOR SECOND-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS ON THE HALF-LINE
نویسنده
چکیده
(Φp(ρ(t)x (t))) + q(t)f(t, x(t), x(t)) = 0, t 6= ti, t ∈ J, ∆x(ti) = Ii(x(ti)), −∆Φp(ρ(ti)x (ti)) = Ji(x(ti)), i = 1, 2, . . . , m, x(0) = ax(ξ), lim t→+∞ ρ(t)x(t) = 0, here J = [0,+∞), Φpx := |x| x, p > 1, 0 = t0 < t1 < · · · < tm < ∞, a > 0, 0 ≤ ξ <∞, aξ < 1, ρ, Ii, Ji, q, f satisfy the following assumptions (H1) ρ ∈ C[0,+∞) ∩ C(0,+∞), ρ(t) > 0 is increasing on [0,+∞), ∫∞ 0 1 ρ(t) dt <∞; (H2) Ii, Ji ∈ C(J, J), ∆x(ti) = x(t + i ) − x(t − i ), where x(t + i ) (respectively x(t − i )) denote the right limit (respectively left limit ) of x(t) at t = ti, ∆Φp(ρ(ti)x (ti)) = Φp(ρ(t + i )x (t+i ))−Φp(ρ(t − i )x (t−i )), where x (t+i ) (respectively x (t−i )) denote the right limit (respectively left limit ) of x(t) at t = ti; (H3) q ∈ L(J, J), f : J × J × J → J is an L-Carathédory function, that is, (i) t→ f(t, x, y) is measurable for any (x, y) ∈ J × J ,
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