Abstract
In this paper, we investigate the existence of positive solutions for a class of singular second-order differential equations with periodic boundary conditions. By using the fixed point theory in cones, the explicit range for λ is derived such that for any λ lying in this interval, the existence of at least one positive solution to the boundary value problem is guaranteed.
Highlights
1 Introduction Reaction-diffusion problems often arise in physics, chemistry, biology, economics, and various engineering fields
The Liebau phenomenon, which is in honor of the physician Liebauh’s pioneering work, is the occurrence of valveless pumping through the application of a periodic force at a place which lies asymmetric with respect to system configuration
2 Preliminaries and lemmas we present some notations and lemmas that will be used in the proof of our main results
Summary
Reaction-diffusion problems often arise in physics, chemistry, biology, economics, and various engineering fields. With appropriate boundary value conditions, the existence of positive solution of equation ( ) is significant and helpful. We discuss the positive solutions of the following periodic boundary value problem (PBVP):
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