Boundary value problems for 2n-th order nonlinear ordinary differential equation

Abstract

The authors consider the 2n-th order ordinary differential equation

together with the boundary conditions

where and are continuous, and λ > 0 is a parameter. They give sufficient conditions for the existence of at least oilt positive solution of the problem (EWB), as well as sufficient conditions for the problem (E)- (B) to have no positive solutions. An example is given to show that their results are sharp.

Keywords:

• Boundary value problems
• Existence of positive solutions
• Higher

AMS Subject Classification:

• 34B15

^∗Corresponding author.

^∗Corresponding author.

Notes

^∗Corresponding author.