Existence and multiplicity of periodic solutions for some second order differential systems with p(t)-Laplacian

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Liang Zhang ◽  
X. Tang
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Least Action Principle ◽  
Differential Systems ◽  
Least Action ◽  
Existence And Multiplicity ◽  
The Least Action Principle

AbstractIn this paper, we deal with the existence and multiplicity of periodic solutions for the p(t)-Laplacian Hamiltonian system. Some new existence theorems are obtained by using the least action principle and minmax methods in critical point theory, and our results generalize and improve some existence theorems.

scholarly journals Existence of Periodic Solutions for a Class of Difference Systems withp-Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Kai Chen ◽  
Qiongfen Zhang
Keyword(s):  
Periodic Solutions ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Minimax Methods ◽  
Difference Systems ◽  
Existence Of Periodic Solutions

By applying the least action principle and minimax methods in critical point theory, we prove the existence of periodic solutions for a class of difference systems withp-Laplacian and obtain some existence theorems.

Periodic solutions of non-autonomous second order systems with (q(t), p(t))-Laplacian

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
Daniel Paşca ◽  
Chun-Lei Tang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Second Order Systems

AbstractUsing the least action principle in critical point theory we obtain some existence results of periodic solutions for (q(t), p(t))-Laplacian systems which generalize some existence results.

Existence of periodic solutions for sublinear second order dynamical system with (q, p)-Laplacian

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Xiaoxia Yang ◽  
Haibo Chen
Keyword(s):  
Dynamical System ◽  
Saddle Point ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Saddle Point Theorem ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Existence Of Periodic Solutions

AbstractIn this paper, some existence theorems are obtained for periodic solutions of second order dynamical system with (q, p)-Laplaician by using the least action principle and the saddle point theorem. Our results improve Pasca and Tang’ results.

scholarly journals Existence and Multiplicity of Periodic Solutions Generated by Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Liu Yang ◽  
Haibo Chen
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Differential Systems ◽  
Existence And Multiplicity ◽  
Infinitely Many Periodic Solutions

We investigate the existence and multiplicity of periodic solutions for a class of second-order differential systems with impulses. By using variational methods and critical point theory, we obtain such a system possesses at least one nonzero, two nonzero, or infinitely many periodic solutions generated by impulses under different conditions, respectively. Recent results in the literature are generalized and significantly improved.

Infinitely many periodic solutions for ordinary p-Laplacian systems

2015 ◽  
Vol 4 (4) ◽  
pp. 251-261 ◽  
Author(s):  
Chun Li ◽  
Ravi P. Agarwal ◽  
Chun-Lei Tang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Minimax Methods ◽  
Infinitely Many Periodic Solutions

AbstractSome existence theorems are obtained for infinitely many periodic solutions of ordinary p-Laplacian systems by minimax methods in critical point theory.

scholarly journals Periodic Solutions for a System of Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Shugui Kang ◽  
Bao Shi
Keyword(s):  
Nonlinear Systems ◽  
Critical Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Second Order ◽  
System Of Difference Equations

This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.

MULTIPLE HOMOCLINICS IN A HAMILTONIAN SYSTEM WITH ASYMPTOTICALLY OR SUPER LINEAR TERMS

2006 ◽  
Vol 08 (04) ◽  
pp. 453-480 ◽  
Author(s):  
YANHENG DING
Keyword(s):  
Hamiltonian System ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Formulation ◽  
Homoclinic Orbits ◽  
Point Theory ◽  
Asymptotically Linear ◽  
Recent Information ◽  
Existence And Multiplicity ◽  
The Matrix

This paper is concerned with homoclinic orbits in the Hamiltonian system [Formula: see text] where H is periodic in t with Hz(t, z) = L(t)z + Rz(t, z), Rz(t, z) = o(|z|) as z → 0. We find a condition on the matrix valued function L to describe the spectrum of operator [Formula: see text] so that a proper variational formulation is presented. Supposing Rz is asymptotically linear as |z| → ∞ and symmetric in z, we obtain infinitely many homoclinic orbits. We also treat the case where Rz is super linear as |z| → ∞ with assumptions different from those studied previously in relative work, and prove existence and multiplicity of homoclinic orbits. Our arguments are based on some recent information on strongly indefinite functionals in critical point theory.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

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