scholarly journals A MULTIPLICITY THEOREM FOR A PERTURBED SECOND-ORDER NON-AUTONOMOUS SYSTEM

2006 ◽  
Vol 49 (2) ◽  
pp. 267-275 ◽  
Author(s):  
Francesca Faraci ◽  
Antonio Iannizzotto
Keyword(s):  
Variational Principle ◽  
Periodic Solutions ◽  
Autonomous System ◽  
Second Order ◽  
Mountain Pass ◽  
Connected Components ◽  
Multiplicity Result ◽  
Global Minima ◽  
Multiplicity Theorem

AbstractIn this paper we establish a multiplicity result for a second-order non-autonomous system. Using a variational principle of Ricceri we prove that if the set of global minima of a certain function has at least $k$ connected components, then our problem has at least $k$ periodic solutions. Moreover, the existence of one more solution is investigated through a mountain-pass-like argument.

scholarly journals Three periodic solutions to an eigenvalue problem for a class of second-order Hamiltonian systems

2003 ◽  
Vol 2003 (18) ◽  
pp. 1037-1045 ◽  
Author(s):  
Giuseppe Cordaro
Keyword(s):  
Eigenvalue Problem ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Open Interval ◽  
Second Order ◽  
Multiplicity Result ◽  
Second Order Hamiltonian Systems

We establish a multiplicity result to an eigenvalue problem related to second-order Hamiltonian systems. Under new assumptions, we prove the existence of an open interval of positive eigenvalues in which the problem admits three distinct periodic solutions.

Existence of Periodic Solution for a Class of Symmetric Superquadratic Second-Order Non-Autonomous Hamiltonian Systems

2014 ◽  
Vol 530-531 ◽  
pp. 609-612
Author(s):  
Qin Jiang ◽  
Sheng Ma
Keyword(s):  
Periodic Solution ◽  
Critical Point ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Fixed Period

In the paper, by the symmetrical Mountain-Pass lemma in critical point theory, the existence of infinitely anti-and odd periodic solutions with a fixed period is obtained for a class of symmetric superquadratic non-autonomous Hamiltonian systems.

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 Periodic solutions to reversible second order autonomous DDEs in prescribed symmetric nonconvex domains

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Zalman Balanov ◽  
Norimichi Hirano ◽  
Wiesław Krawcewicz ◽  
Fangfang Liao ◽  
Adrian Murza
Keyword(s):  
Periodic Solutions ◽  
Second Order ◽  
Nonconvex Domains
Sign in / Sign up

Export Citation Format

Share Document