Monotone Positive Solution of Nonlinear Third-Order BVP with Integral Boundary Conditions. (2nd November 2010) - Sun Sun, Jian-Ping Jian-Ping; Li Li, Hai-Bao Hai-Bao
Abstract : This paper is concerned with the following third-order boundary value problem with integral boundary conditions u ′′′ ( t ) + f ( t, u ( t ), u ′ ( t ) ) = 0, t ∈ [ 0, 1 ] ; u ( 0 ) = u ′ ( 0 ) = 0, u ′ ( 1 ) = ∫ 0 1 g ( t ) u ′ ( t ) d t, where f ∈ C ( [ 0, 1 ] × [ 0, + ∞ ) × [ 0, + ∞ ), [ 0, + ∞ ) ) and g ∈ C ( [ 0, 1 ], [ 0, + ∞ ) ) . By using the Guo-Krasnoselskii fixed-point theorem, some sufficient conditions are obtained for the existence and nonexistence of monotone positive solution to the above problem.