January  2002, 8(1): 39-54. doi: 10.3934/dcds.2002.8.39

Guiding-like functions for periodic or bounded solutions of ordinary differential equations

1. 

Institut Mathématique Pure et Appliquée, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

2. 

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, United States

Received  January 2001 Revised  May 2001 Published  October 2001

We state and prove some extensions of the fundamental theorem of the method of guiding functions for periodic and for bounded solutions of ordinary differential systems. Those results unify and generalize previous results of Krasnosel'skii, Perov, Mawhin, Walter and Gossez.
Citation: Jean Mawhin, James R. Ward Jr. Guiding-like functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 39-54. doi: 10.3934/dcds.2002.8.39
[1]

Christian Pötzsche. Nonautonomous continuation of bounded solutions. Communications on Pure & Applied Analysis, 2011, 10 (3) : 937-961. doi: 10.3934/cpaa.2011.10.937

[2]

Jean Mawhin. Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1065-1076. doi: 10.3934/dcdss.2013.6.1065

[3]

Zalman Balanov, Meymanat Farzamirad, Wieslaw Krawcewicz, Haibo Ruan. Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 923-960. doi: 10.3934/dcds.2006.16.923

[4]

Marc Henrard. Homoclinic and multibump solutions for perturbed second order systems using topological degree. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 765-782. doi: 10.3934/dcds.1999.5.765

[5]

Dong Ye, Feng Zhou. Invariant criteria for existence of bounded positive solutions. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 413-424. doi: 10.3934/dcds.2005.12.413

[6]

Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. Bounded solutions of the Boltzmann equation in the whole space. Kinetic & Related Models, 2011, 4 (1) : 17-40. doi: 10.3934/krm.2011.4.17

[7]

Franco Obersnel, Pierpaolo Omari. Multiple bounded variation solutions of a capillarity problem. Conference Publications, 2011, 2011 (Special) : 1129-1137. doi: 10.3934/proc.2011.2011.1129

[8]

Manuel Núñez. Existence of solutions of the equations of electron magnetohydrodynamics in a bounded domain. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 1019-1034. doi: 10.3934/dcds.2010.26.1019

[9]

Maria Assunta Pozio, Alberto Tesei. On the uniqueness of bounded solutions to singular parabolic problems. Discrete & Continuous Dynamical Systems - A, 2005, 13 (1) : 117-137. doi: 10.3934/dcds.2005.13.117

[10]

Luisa Malaguti, Cristina Marcelli. Existence of bounded trajectories via upper and lower solutions. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 575-590. doi: 10.3934/dcds.2000.6.575

[11]

Adnan Ben Aziza, Mohamed Ben Chrouda. Characterization for the existence of bounded solutions to elliptic equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 1157-1170. doi: 10.3934/dcds.2019049

[12]

Shigeki Akiyama. Strong coincidence and overlap coincidence. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5223-5230. doi: 10.3934/dcds.2016027

[13]

Ezzeddine Zahrouni. On the Lyapunov functions for the solutions of the generalized Burgers equation. Communications on Pure & Applied Analysis, 2003, 2 (3) : 391-410. doi: 10.3934/cpaa.2003.2.391

[14]

Mihaela Roxana Nicolai, Dan Tiba. Implicit functions and parametrizations in dimension three: Generalized solutions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2701-2710. doi: 10.3934/dcds.2015.35.2701

[15]

José Luis Bravo, Manuel Fernández, Antonio Tineo. Periodic solutions of a periodic scalar piecewise ode. Communications on Pure & Applied Analysis, 2007, 6 (1) : 213-228. doi: 10.3934/cpaa.2007.6.213

[16]

Xiaoyan Lin, Xianhua Tang. Solutions of nonlinear periodic Dirac equations with periodic potentials. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 2051-2061. doi: 10.3934/dcdss.2019132

[17]

Christian Pötzsche. Nonautonomous bifurcation of bounded solutions II: A Shovel-Bifurcation pattern. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 941-973. doi: 10.3934/dcds.2011.31.941

[18]

Yiqian Wang. Boundedness of solutions in a class of Duffing equations with a bounded restore force. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 783-800. doi: 10.3934/dcds.2006.14.783

[19]

Yuan Guo, Xiaofei Gao, Desheng Li. Structure of the set of bounded solutions for a class of nonautonomous second order differential equations. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1607-1616. doi: 10.3934/cpaa.2010.9.1607

[20]

Christian Pötzsche. Nonautonomous bifurcation of bounded solutions I: A Lyapunov-Schmidt approach. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 739-776. doi: 10.3934/dcdsb.2010.14.739

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]