Existence of positive solutions for a nonlinear fourth order boundary value problem
Ruyun Ma (2003)
Annales Polonici Mathematici
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We study the existence of positive solutions of the nonlinear fourth order problem , u(0) = u’(0) = u”(1) = u”’(1) = 0, where a: [0,1] → ℝ may change sign, f(0) < 0, and λ < 0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.