Existnence and nonexistence of positive solutions of fourth order nonlinear boundary value problems

Abstract

The authors consider booundary value problems for fourth order ordinary differential equations of the form

with the boundary conditions

or

They give sufficient conditions for the problems (E)-(B₁) and (E)-(B₂) to have at least one positive solutions. They also give sufficient conditions for these problems to have no positive solutions. Examples to illustrate that the results are sharp are also included.

Keywords:

• Existence of psitive solutions
• fourth order equations
• nonexistence of positive solutions
• nonlinear boundary value problems

AMS:

• 34B15