Monotone and convex positive solutions for fourth-order multi-point boundary value problems
1 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China
2 Department of Mathematics, Hefei Normal University, Hefei, Anhui Province 230061, PR China
Boundary Value Problems 2011, 2011:21 doi:10.1186/1687-2770-2011-21Published: 5 September 2011
The existence results of multiple monotone and convex positive solutions for some fourth-order multi-point boundary value problems are established. The nonlinearities in the problems studied depend on all order derivatives. The analysis relies on a fixed point theorem in a cone. The explicit expressions and properties of associated Green's functions are also given.
MSC: 34B10; 34B15.