Weak singularities may help periodic solutions to exist

By Pedro J. Torres. 2007

137 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d625fb9b60c7b600a887dc4e93c8d55f1df353da

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

In Control and Systems Engineering

1. Jifeng Chu
2. Haiyan Wang
3. Daniel Franco
4. N. Fan
5. Pedro J. Torres
6. J. J. Nieto
7. Meirong Zhang
8. Emile-Franc Doungmo Goufo

In Numerical Analysis

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

Citations in the corpus

• Applications of Schauder's fixed point theorem to singular differential equations (2007, background): “2 under strong force conditions was posed as an open problem in [16].”
• Impulsive periodic solutions of first‐order singular differential equations (2008, result): “We also remark that for the periodic singular problems, even without impulse effects, similar results are more restrictive and only few references [5, 14, 30] can be found.”
• 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 [”
• 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 of second order non-autonomous singular dynamical systems (2007, background): “Our view point sheds some new light on problems with weak force potentials and we prove that in some situations weak singularities may stimulate the existence of periodic solutions, just as pointed out in [28] for the scalar case.”
• Periodic solutions of singular systems without the strong force condition (2007, methodology): “The proof would be almost the same as in Theorem 4 of [14], so we leave it to the reader.”