Existence of positive periodic solutions of some differential equations of order n (n≥2)

Jan Ligęza

Published: 2009-09-30

Vol. 23 (2009)

Existence of positive periodic solutions of some differential equations of order n (n≥2)

Jan Ligęza

Abstract

We study the existence of positive periodic solutions of the equations
x⁽ⁿ⁾(t) − p(t)x(t) + μf(t, x(t), x'(t), . . . , x⁽ⁿ⁻¹⁾(t)) = 0,
x⁽ⁿ⁾(t) + p(t)x(t) = μf(t, x(t), x'(t), . . . , x⁽ⁿ⁻¹⁾(t)),
where n≥2, μ>0, p: (-∞,∞)→(0,∞) is continuous and 1–periodic, f is a continuous function and 1–periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.

Keywords:

positive solutions , boundary value problems , cone , Krasnosielski fixed point theorem , Green’s function

Download files

PDF

Citation rules

Ligęza, J. (2009). Existence of positive periodic solutions of some differential equations of order n (n≥2). Annales Mathematicae Silesianae, 23, 61–81. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14045

Similar Articles

Wojciech Surówka, A discrete form of Jordan curve theorem , Annales Mathematicae Silesianae: Vol. 7 (1993)
Anita Tomar, Meena Joshi, Results in strongly minihedral cone and scalar weighted cone metric spaces and applications , Annales Mathematicae Silesianae: Vol. 35 No. 2 (2021)
Jan Ligęza, Existence of generalized, positive and periodic solutions for some differential equations of order II , Annales Mathematicae Silesianae: Vol. 28 (2014)
Milan Tvrdý, Linear boundary value problems for generalized differential equations , Annales Mathematicae Silesianae: Vol. 14 (2000)
Binayak S. Choudhury, Nikhilesh Metiya, Sunirmal Kundu, Debashis Khatua, Existence, data dependence and stability of fixed points of multivalued maps in incomplete metric spaces , Annales Mathematicae Silesianae: Vol. 37 No. 1 (2023)
Svatoslav Staněk, On the existence of two solutions of functional boundary value problems , Annales Mathematicae Silesianae: Vol. 14 (2000)
Mohammad Asim, Mohammad Imdad, Fixed point and best proximity point results in PIV-S-metric spaces , Annales Mathematicae Silesianae: 2024: Online First
Jan Ligęza, Existence of positive solutions of some integral equations , Annales Mathematicae Silesianae: Vol. 18 (2004)
Li Lin Huang, Hou Yu Zhao, Convex solutions of an iterative functional differential equation , Annales Mathematicae Silesianae: 2024: Online First
Damian Wiśniewski, The behaviour of weak solutions of boundary value problems for linear elliptic second order equations in unbounded cone-like domains , Annales Mathematicae Silesianae: Vol. 30 (2016)

1 2 3 4 5 6 7 8 9 10 > >>

You may also start an advanced similarity search for this article.

References

1. Agarwal R.P., Grace S.R., O’Regan D., Existence of positive solutions of semipositone Fredholm integral equations, Funkcial. Ekvac. 45 (2002), 223–235.
2. Agarwal R.P., O’Regan D., Wang P.J.Y., Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999.
3. Agarwal R.P., O’Regan D., Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001.
4. Cabada A., The method of lower and upper solutions for second, third, fourth and higher order boundary value problems, J. Math. Anal. Appl. 185 (1994), 302–320.
5. Deimling K., Nonlinear Functional Analysis, Springer, New York, 1985.
6. Guo D., Laksmikannthan V., Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988.
7. Lasota A., Opial Z., Sur les solutions périodiques des équations différentielles ordinaires, Ann. Polon. Math. 16 (1964), 69–94.
8. Rektorys K., Variational Methods in Mathematics, Science and Engineering, D. Reidel Publishing Co., Dordrecht, 1980.
9. Śeda V., Nieto J.J., Gera M., Periodic boundary value problems for nonlinear higher order ordinary differential equations, Appl. Math. Comput. 48 (1992), 71–82.
10. Torres P.J., Existence of one–signed periodic solution of some second–order differential equations via a Krasnosielskii fixed point theorem, J. Differential Equations 190 (2003), 643–662.
11. Zima M., Positive Operators in Banach Spaces and Their Applications, Wydawnictwo Uniwersytetu Rzeszowskiego, Rzeszów, 2005. Google Scholar

Vol. 23 (2009)
Published: 2009-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit