Non-constant periodic solutions for second order Hamiltonian system with a p-Laplacian

2012 ◽  
Vol 62 (2) ◽  
Author(s):  
Xingyong Zhang ◽  
Xianhua Tang
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Linking Theorem ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractIn this paper, some existence theorems are obtained for nonconstant periodic solutions of second order Hamiltonian system with a p-Laplacian by using the Linking Theorem.

Non-constant Periodic Solutions for Second Order Hamiltonian System Involving the p-Laplacian

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Xingyong Zhang ◽  
Xianhua Tang
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractIn this paper, some existence theorems are obtained for non-constant periodic solutions of second order Hamiltonian system involving the p-Laplacian by using the linking method. Our results generalize and improve several known results in the literature.

Subharmonics near an equilibrium for some second-order Hamiltonian systems

1993 ◽  
Vol 123 (5) ◽  
pp. 819-834 ◽  
Author(s):  
Patricio L. Felmer ◽  
Elves A. de B. e Silva
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Second Order ◽  
Point Of View ◽  
Subharmonic Solutions ◽  
Second Order Hamiltonian Systems ◽  
Order Hamiltonian System ◽  
Existence Of Periodic Solutions ◽  
Image Position ◽  
Second Order Hamiltonian System

SynopsisThis work is devoted to the study of subharmonic solutions of a second-order Hamiltonian systemnear an equilibrium point, say q = 0. The problem of existence of periodic solutions from the global point of view is also considered.This problem has been studied for the case where the potential is positive and superquadratic. In this work a potential V that has change in sign is considered. The potential is decomposed aswhere P is homogeneous, superquadratic and nondegenerate, and is of higher order near 0. In this paper the existence is shown of a sequence of subharmonic solutions of the equation above that converges to the equilibrium, such that their minimal periods converge to infinity.This problem is approached from a variational point of view. Existence of subharmonic and periodic solutions is obtained via minimax techniques.

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