Abstract
This article studies the existence of positive periodic solutions for a class of strongly coupled differential systems. By applying the fixed point theory, several existence results are established. Our main findings generalize and complement those in the literature studies.
Highlights
We are concerned with the existence of positive periodic solutions of the strongly coupled differential systems: Lixi fi t, x1, x2 + ei(t), i 1, 2, (1)
During the past few decades, the fixed point theory has been widely adopted to investigate the nonperiodic coupled differential systems, and researchers have mainly concentrated on the existence and multiplicity of positive solutions [1,2,3]
What is worth mentioning is the results obtained in [5, 6, 11, 12], where the authors show, under some circumstances, weak singularities are helpful to seek out periodic solutions for singular equations [5] and singular coupled systems [11]
Summary
We are concerned with the existence of positive periodic solutions of the strongly coupled differential systems: Lixi fi t, x1, x2 + ei(t), i 1, 2, (1)where Lixi x′′i + pi(t)x′i + qi(t)xi is a linear differential operator with pi, qi ∈ L1(R/TZ, R). We are concerned with the existence of positive periodic solutions of the strongly coupled differential systems: Lixi fi t, x1, x2 + ei(t), i 1, 2, (1) What is worth mentioning is the results obtained in [5, 6, 11, 12], where the authors show, under some circumstances, weak singularities are helpful to seek out periodic solutions for singular equations [5] and singular coupled systems [11]. Erefore, motivated by the aforementioned papers, we shall establish the existence of positive periodic
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