scholarly journals Twist periodic solutions of second order singular differential equations

2009 ◽  
Vol 355 (2) ◽  
pp. 830-838 ◽  
Author(s):  
Jifeng Chu ◽  
Ming Li
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Second Order ◽  
Singular Differential Equations

scholarly journals PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

scholarly journals IMPULSIVE PERIODIC SOLUTIONS FOR SINGULAR PROBLEMS VIA VARIATIONAL METHODS

2012 ◽  
Vol 86 (2) ◽  
pp. 193-204 ◽  
Author(s):  
JUNTAO SUN ◽  
DONAL O’REGAN
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Periodic Solutions ◽  
Mountain Pass Theorem ◽  
Second Order ◽  
Mountain Pass ◽  
Singular Problems ◽  
Singular Differential Equations

AbstractIn this paper we study impulsive periodic solutions for second-order nonautonomous singular differential equations. Our proof is based on the mountain pass theorem. Some recent results in the literature are extended.

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

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