Positive solutions for the third-order boundary value problems with the second derivatives
1 College of Electrical Engineering and Information, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, PR China
2 College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, PR China
Boundary Value Problems 2012, 2012:34 doi:10.1186/1687-2770-2012-34Published: 26 March 2012
By using the fixed-point index theory in a cone and defining a linear operator, we obtain the existence of at least one positive solution for the third-order boundary value problem with integral boundary conditions
where f : [0, 1] × R+ × R- → R+ is a nonnegative function. The associated Green's function for the above problem is also used, and a new reproducing cone also used.