Positive Solution for Fourth Order Boundary Value Problem

DOI : http://dx.doi.org/10.13005/msri/040105

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In this paper, we investigate the problem of existence of positive solutions for the nonlinear fourth order boundary value problem: D4u(t) = la(t)f(u(t)), 0 < t < 1, u(0) = u"(0) = u'(1) = u"'(1) = 0, where l is a positive parameter. By using Krasnoesel?skii?s fixed point theorem of cone, we establish various results on the existence of positive solutions of the boundary value problem. Under various assumptions on a(t) and f(u(t)), we give the intervals of the parameter l which yield the existence of

Fourth order boundary value problem; Krasnoesel?skii?s fixed point theorem