A multiplicity result for a generalized Sturm–Liouville problem on time scales

Abstract

By applying the fixed point theorem in cones, a new and general result on the existence of positive solutions to second-order generalized Sturm–Liouville boundary value problem on a time scale 𝕋 is obtained. The first order Δ-derivative is involved in the nonlinear term f explicitly.

Keywords:

• Sturm–Liouville problem
• cone
• fixed point
• positive solution
• time scales

AMS Subject Classification (2000)::

• 34B15
• 39A10

Acknowledgements

The author would like to thank the referees for their very valuable comments and suggestions to the improvement of this paper.