Positive Solutions of a Nonlinear m-Point Integral Boundary Value Problem
نویسنده
چکیده
We study sufficient conditions for the existence of positive solutions to the m-point integral boundary value problem u + a(t)f (u) = 0, t∈ (0, 1), u(0) = 0, u(1) = m−1 i=1 α i η i η i−1 u(s)ds, where 0 = η 0 < η 1 < η 2 < · · · < η m−2 < η m−1 = 1, 0 < m−1 i=1 α i (η 2 i − η 2 i−1) < 2, α i ≥ 0 for i ∈ {1,. .. , m − 3} ∪ {m − 1} and α m−2 > 0. a ∈ C([0, 1], [0, ∞)) and f ∈ C([0, ∞), [0, ∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.
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