Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions. (3rd August 2010) - Ma, Ruyun; Chen, Tianlan
Abstract : We study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, u ( 4 ) ( t ) = f ( t, u ( t ), u ′′ ( t ) ), t ∈ ( 0, 1 ), u ( 0 ) = ∫ 0 1 g ( s ) u ( s ) d s, u ( 1 ) = 0, u ′′ ( 0 ) = ∫ 0 1 h ( s ) u ′′ ( s ) d s, u ′′ ( 1 ) = 0, wheref : [ 0, 1 ] × [ 0, + ∞ ) × ( - ∞, 0 ] → [ 0, + ∞ ) is continuous, g, h ∈ L 1 [ 0, 1 ] are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques.