Singular nonlinear boundary value problems

Abstract

We study nonlinear singular Sturm-Liouville bondary value prob lems associated with the operator , special cases of which come up in connection with the radial Laplace operator, and prove existence and uniqueness theorems under asymptotic non- resonance conditions on the slope of the nonlinear term with respect to the dependent variable. For the underlying linear problemsis allowed; nevertheless they have a pure point spectrum as in the classical case. In our treatment the Prüfer transformation plays an essential role. Our results apply in the case where Dirchlet's problem with radial data is considered in a ball, whereas this problem on an annulus leads to regular Sturm-Liouville problems.

Keywords:

• Ordinary differential equations
• nonlinear boundary value problems
• Sturm-Liouville type

AMS:

• 34B05
• 34B15
• 354J65
• 34E0