×

Existence of positive periodic solutions for a class of non-autonomous fourth-order ordinary differential equations. (Chinese. English summary) Zbl 1463.34159

Summary: This paper studies the existence of positive periodic solutions for a class of non-autonomous fourth-order ordinary differential equations \[{u^{(\mathrm{iv})}} + pu'' + a (x){u^n} - b (x){u^{n+1}} - c (x){u^{n+2}} = 0,\] where \(p \ge -1\), \(n\) is a finite positive integer, \(a (x)\), \(b (x)\), \(c (x)\) are continuous \(T\)-periodic functions. By using Mawhin’s continuation theorem, the existence of positive periodic solutions for this kind of equations is proved.

MSC:

34C25 Periodic solutions to ordinary differential equations
37C60 Nonautonomous smooth dynamical systems
47N20 Applications of operator theory to differential and integral equations
PDFBibTeX XMLCite
Full Text: DOI