Existence of Positive Solutions for Nonlocal Fourth-Order Boundary Value Problem with Variable Parameter

By using the Krasnoselskii's fixed point theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundary value problem with variable parameter u((4)) (t) + B(t) u"(t) = lambda f (t, u(t), u" (t)), 0 < t < 1, u(0) = u(1) = integral(1)(0) p(s) u (s) ds, u" (0) = u"(1) = integral(1)(0)q (s) u" (s) ds is considered, where p, q is an element of L(1) [0,1], lambda > 0 is a parameter, and B is an element of C [0, 1], f is an element of C([0, 1] x [0, infinity) x (-infinity, 0], [0, infinity)).