American Institute of Mathematical Sciences

Advanced
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

Jean Mawhin 1, and  James R. Ward Jr 2,

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.
Keywords: coincidence degree., Guiding functions, periodic solutions, bounded solutions.
Mathematics Subject Classification: 34C25, 34D4.
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]

Gang Li, Fen Gu, Feida Jiang. Positive viscosity solutions of a third degree homogeneous parabolic infinity Laplace equation. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1449-1462. doi: 10.3934/cpaa.2020071
[5]

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
[6]

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
[7]

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
[8]

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
[9]

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
[10]

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
[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]

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
[13]

Shigeki Akiyama. Strong coincidence and overlap coincidence. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5223-5230. doi: 10.3934/dcds.2016027
[14]

Chunyan Ji, Xue Yang, Yong Li. Periodic solutions for SDEs through upper and lower solutions. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020122
[15]

Guo Lin, Shuxia Pan. Periodic traveling wave solutions of periodic integrodifference systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3005-3031. doi: 10.3934/dcdsb.2020049
[16]

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
[17]

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
[18]

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
[19]

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
[20]

Ján Eliaš, Masayasu Mimura, Ryunosuke Mori. Asymptotic behavior of solutions of Aoki-Shida-Shigesada model in bounded domains. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020082

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (31)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences