EXISTENCE OF SOLUTIONS FOR A SECOND ORDER THREE POINT BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS ON A HALF LINE

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In this paper, we consider the second order three point boundary value problem with integral bounday conditions on a half-line of the form u”(t) + q(t)f(t, u(t), u'(t)) = 0, t∈ (0,+∞), u(0) − au’ (0) = λη 0 u(s)ds, lim t→+∞ u (t) = u (+∞) = λ η0 u(s)ds, where λ > 0, 0 < λη < 1, a > 0, q : (0,+∞) → (0,+∞), f : [0,+∞) × R × R → R is continuous and satisfies Nagumo’s condition. We employ the Schauder’s fixed point theorem, the upper and lower solution method and topological degree theories to show the existence of at least one solution and then existence of three solutions of the above boundary value problem. Finally, we have shown the importance of our results through an examples.

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