Czechoslovak Mathematical Journal, first online, pp. 1-19
Positive periodic solutions to super-linear second-order ODEs
Jiří Šremr
Received March 23, 2023. Published online March 28, 2024.
Abstract: We study the existence and uniqueness of a positive solution to the problem $u''=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega),\ u'(0)=u'(\omega)$ with a super-linear nonlinearity and a nontrivial forcing term $f$. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.
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Affiliations: Jiří Šremr, Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic, e-mail: sremr@fme.vutbr.cz
