Periodic Orbits of Radially Symmetric Systems with a Singularity: the Repulsive Case

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Alessandro Fonda ◽  
Rodica Toader
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Large Amplitude ◽  
Topological Degree ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Periodic Forcing ◽  
The Third ◽  
Large Angular Momentum ◽  
Symmetric Systems

AbstractWe study radially symmetric systems with a singularity of repulsive type. In the presence of a radially symmetric periodic forcing, we show the existence of three distinct families of subharmonic solutions: One oscillates radially, one rotates around the origin with small angular momentum, and the third one with both large angular momentum and large amplitude. The proofs are carried out by the use of topological degree theory.

scholarly journals Periodic Orbits of Radially Symmetric Keplerian-Like Systems with a Singularity

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Shengjun Li ◽  
Yuming Zhu
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Large Amplitude ◽  
Topological Degree ◽  
Degree Theory ◽  
The Other ◽  
Topological Degree Theory ◽  
Families Of Periodic Orbits ◽  
Large Angular Momentum

We study planar radially symmetric Keplerian-like systems with repulsive singularities near the origin and with some semilinear growth near infinity. By the use of topological degree theory, we prove the existence of two distinct families of periodic orbits; one rotates around the origin with small angular momentum, and the other one rotates around the origin with both large angular momentum and large amplitude.

scholarly journals LOCATING PERIODIC ORBITS BY TOPOLOGICAL DEGREE THEORY

2003 ◽  
Author(s):  
C. POLYMILIS ◽  
G. SERVIZI ◽  
G. TURCHETTI ◽  
CH. SKOKOS ◽  
M. N. VRAHATIS
Keyword(s):  
Periodic Orbits ◽  
Topological Degree ◽  
Degree Theory ◽  
Topological Degree Theory

scholarly journals Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 218 ◽  
Author(s):  
Muhammad Sher ◽  
Kamal Shah ◽  
Michal Fečkan ◽  
Rahmat Ali Khan
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Topological Degree ◽  
Degree Theory ◽  
Qualitative Theory ◽  
Proportional Delay ◽  
Topological Degree Theory ◽  
Fractional Order Differential Equations ◽  
Delay Differential ◽  
Stability Results

With the help of the topological degree theory in this manuscript, we develop qualitative theory for a class of multi-terms fractional order differential equations (FODEs) with proportional delay using the Caputo derivative. In the same line, we will also study various forms of Ulam stability results. To clarify our theocratical analysis, we provide three different pertinent examples.

scholarly journals Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This paper is concerned with the existence of positive solutions for a class of boundary value problems of fractional differential equations with parameter. The main tools used here are bifurcation techniques and topological degree theory. Finally, an example is worked out to demonstrate the main result.

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