Multiplicity of positive periodic solutions to superlinear repulsive singular equations

By Daqing Jiang, Jifeng Chu, Meirong Zhang. 2005

166 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1d130c1eef91e226bdd72602425f833fd83d2bd8

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 Geometry and Topology

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

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

• Periodic solutions of singular systems without the strong force condition (2007, background): “As a final comment, let us emphasize that our standing hypothesis (A) (nonnegativeness) is weaker than the required condition in [15, 7, 9] (positiveness of the Green’s function) and allows, for instance, the critical case a(t) ≡ π T .”
• Periodic Solutions of Equations of Emarkov-Pinney Type (2006, unknown): “See [4, 9, 10, 11, 12, 13].”
• Periodic solutions of second order non-autonomous singular dynamical systems (2007, background): “Therefore the new results generalize and improve those in [10,11] and those in [15] even for the scalar cases.”
• Positive periodic solutions of singular systems with a parameter (2010, methodology): “More recently, the method of lower and upper solutions, the Schauder’s fixed point theorem and the Krasnoselskii fixed point theorem in a cone have been employed to investigate the existence of positive periodic solutions of the systems [2,3,4,11,12,14,15,19,25,26,27].”
• Applications of Schauder's fixed point theorem to singular differential equations (2007, methodology): “In [9, 15], the existence results are based on the positivity of G(t, s), which plays a very important role in employing some fixed point theorems in cones for completely continuous operators.”
• Weak singularities may help periodic solutions to exist (2007, background): “Since then, the strong force condition became standard in the related works, see, for instance, [3,5,6,10,11,13–16,18,24,27], the recent review [17] and their bibliographies.”
• Periodic solutions for second order singular damped differential equations (2012, methodology): “1) using a nonlinear alternative of Leray-Schauder, which has been used in [7, 8, 20].”
• 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.”