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where n ≥ , f : [, ]× (R+)n– → R+ is continuous in which R+ = [,+∞), A and B are right continuous on [, ), left continuous at t = , and nondecreasing on [, ], withA() = B() = ; ∫   v(s)dA(s) and ∫   v(s)dB(s) denote the Riemann-Stieltjes integrals of v with respect to A and B, respectively. Boundary value problems (BVPs for short) for(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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