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In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions to m-point boundary value problem for the second order differential equation with an advanced argument {u"(t)+a(t)f(u(h(t)))=0, t isin (0,1), u(0)=0, Sigmai=1m-2 kiu(xii)=u(1), where 0=xi0<xi1<hellip<xim-2<xim-1=1.
In this paper, the second order m-point boundary value problem u''(t) + a(t)u'(t) + f{t,u) = 0, 0 les t les 1, u'(0) -m-2Sigmai=1 kiu'(xii) = 0, u(1) = 0 is studied, where k{ > 0(i = 1, 2,..., m-2), 0 < xi1< xi2 < ... < xim-2 < 1. We obtain the existence of at least three positive solutions by using the Leggett-Williams fixed point theorem and the properties.
This paper is devoted to study existence of multiple periodic positive solutions for a class of nonautonomous functional differential equations with impulse actions at fixed moments. The main results here is established by employing the theory of fixed point index in cones.
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