Periodic solutions of singular systems without the strong force condition

By Daniel Franco, Pedro J. Torres. 2007

61 citations recorded by the source corpus.

. We present sufficient conditions for the existence of at least a non-collision periodic solution for singular systems under weak force conditions. We deal with two different types of systems. First, we assume that the system is generated by a potential, and then we consider systems without such hypothesis. In both cases we use the same technique based on Schauder fixed point theorem. Recent results in the literature are significantly improved.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3810b1edfef9c2bfd9811e81b1ef8d2164e010ab

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Haiyan Wang
2. N. Fan
3. Jifeng Chu
4. Pedro J. Torres
5. Daniel Franco
6. J. J. Nieto
7. Ruyun Ma
8. Meirong Zhang

In Numerical Analysis

1. Haiyan Wang
2. Jifeng Chu
3. N. Fan
4. Pedro J. Torres
5. Daniel Franco
6. J. J. Nieto
7. Meirong Zhang
8. Ruyun Ma

Citations in the corpus

• Periodic solutions of second order non-autonomous singular dynamical systems (2007, unknown): “All rights reserved. doi:10.1016/j.jde.2007.05.007”
• Positive periodic solutions of singular systems with a parameter (2010, background): “However, more recently, the existence of positive periodic solutions of the singular systems has been established with a weak force condition [3,4,11,12,20,21,26,27].”
• Periodic solutions for second order singular damped differential equations (2012, methodology): “Some classical tools have been used to study singular differential equations in the literature, including the method of upper and lower solutions [2, 25], degree theory [30, 31, 33], some fixed point theorems in cones for completely continuous operators [11, 26, 27], Schauder’s fixed point theorem [”