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This paper investigates the second-order multipoint boundary value problem on the half-line u′′ t f t, u t ,u′ t 0, t ∈ R , αu 0 − βu′ 0 − ∑ni 1 kiu ξi a ≥ 0, limt→ ∞u′ t b > 0, where α > 0, β > 0, ki ≥ 0, 0 ≤ ξi < ∞ i 1, 2, . . . , n , and f : R × R × R → R is continuous. We establish sufficient conditions to guarantee the existence of unbounded solution(More)
This paper investigates the higher order differential equations with nonlocal boundary conditions ⎧ ⎪ ⎨ ⎪ ⎩ u (n) (t) + f (t, u(t), u (n–2) (t)) = 0, t ∈ (0, 1), u(0) = u (0) = · · · = u (n–3) (0) = 0, u (n–2) (0) = 1 0 u (n–2) (s) dA(s), u (n–2) (1) = 1 0 u (n–2) (s) dB(s). The existence results of multiple monotone positive solutions are obtained by means(More)
and Applied Analysis 3 and integrating over [ρ(a), T , we get p (r) θ Δ (r) = p (ρ (a)) θ Δ (ρ (a)) + ∫ r ρ(a) q (t) θ (t) ∇t. (22) Since p(ρ(a)) > 0, θΔ(ρ(a)) ≥ 0, q(t) > 0, and θ(t) > 0, we obtain p(r)θΔ(r) > 0. Thus, we determine θΔ(r) > 0. This contradiction shows that the solution θ(t) is strictly increasing and positive on [ρ(a), T as desired. Similar(More)
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