Monotone Iterative Technique and Symmetric Positive Solutions to Fourth-Order Boundary Value Problem with Integral Boundary Conditions. (18th August 2014) - Pang, Huihui; Cai, Chen
Abstract : The purpose of this paper is to investigate the existence of symmetric positive solutions for a class of fourth-order boundary value problem: u 4 ( t ) + β u ′ ′ ( t ) = f ( t, u ( t ), u ′ ′ ( t ) ), 0 < t < 1, u ( 0 ) = u ( 1 ) = ∫ 0 1 ‍ p ( s ) u ( s ) d s, u ′ ′ ( 0 ) = u ′ ′ ( 1 ) = ∫ 0 1 ‍ q s u ′ ′ ( s ) d s, where p, q ∈ L 1 [ 0, 1 ], f ∈ C ( [ 0, 1 ] × [ 0, ∞ ) × ( - ∞, 0 ], [ 0, ∞ ) ) . By using a monotone iterative technique, we prove that the above boundary value problem has symmetric positive solutions under certain conditions. In particular, these solutions are obtained via the iteration procedures.