Heteroclinic orbits in plane dynamical systems

Luisa Malaguti; Cristina Marcelli

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 3, page 183-200
  • ISSN: 0044-8753

Abstract

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We consider general second order boundary value problems on the whole line of the type u ' ' = h ( t , u , u ' ) , u ( - ∞ ) = 0 , u ( + ∞ ) = 1 , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the ( u , u ' ) plane dynamical system.

How to cite

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Malaguti, Luisa, and Marcelli, Cristina. "Heteroclinic orbits in plane dynamical systems." Archivum Mathematicum 038.3 (2002): 183-200. <http://eudml.org/doc/248945>.

@article{Malaguti2002,
abstract = {We consider general second order boundary value problems on the whole line of the type $u^\{\prime \prime \}=h(t,u,u^\{\prime \})$, $u(-\infty )=0, u(+\infty )=1$, for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the $(u,u^\{\prime \})$ plane dynamical system.},
author = {Malaguti, Luisa, Marcelli, Cristina},
journal = {Archivum Mathematicum},
keywords = {nonlinear boundary value problems; heteroclinic solutions; lower and upper solutions; singular boundary value problems; nonlinear boundary value problems; heteroclinic solutions; lower and upper solutions; singular boundary value problems},
language = {eng},
number = {3},
pages = {183-200},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Heteroclinic orbits in plane dynamical systems},
url = {http://eudml.org/doc/248945},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Malaguti, Luisa
AU - Marcelli, Cristina
TI - Heteroclinic orbits in plane dynamical systems
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 3
SP - 183
EP - 200
AB - We consider general second order boundary value problems on the whole line of the type $u^{\prime \prime }=h(t,u,u^{\prime })$, $u(-\infty )=0, u(+\infty )=1$, for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the $(u,u^{\prime })$ plane dynamical system.
LA - eng
KW - nonlinear boundary value problems; heteroclinic solutions; lower and upper solutions; singular boundary value problems; nonlinear boundary value problems; heteroclinic solutions; lower and upper solutions; singular boundary value problems
UR - http://eudml.org/doc/248945
ER -

References

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  1. Cahn J. W., Mallet-Paret J., Van Vleck E. S., Traveling wave solutions for systems of ODEs on a two-dimensional spatial lattice, SIAM J. Appl. Math. 59 (1999), 455–493. (1999) Zbl0917.34052MR1654427
  2. Chow S. N., Lin X. B., Mallet-Paret J., Transition layers for singularly perturbed delay differential equations with monotone nonlinearities, J. Dynam. Differential Equations 1 (1989), 3–43. (1989) Zbl0684.34071MR1010959
  3. Hsu C. H., Lin, S S., Existence and multiplicity of traveling waves in a lattice dynamical system, J. Diffetrential Equations 164 (2000), 431–450. Zbl0954.34029MR1765570
  4. Huang W., Monotonicity of heteroclinic orbits and spectral properties of variational equations for delay differential equations, J. Differential Equations 162 (2000), 91–139. Zbl0954.34071MR1741874
  5. Erbe L., Tang M., Structure of positive radial solutions of semilinear elliptic equations, J. Differential Equations 133 (1997), 179–202. (1997) Zbl0871.34023MR1427849
  6. Malaguti L., Marcelli C., Existence of bounded trajectories via upper and lower solutions, Discrete Contin. Dynam. Systems 6 (2000), 575–590. Zbl0979.34019MR1757388
  7. Malaguti L., Marcelli C., Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms, Math. Nachr. 242 (2002). Zbl1016.35036MR1916855
  8. Marcelli C., Rubbioni P., A new extension of classical Müller’s theorem, Nonlinear Anal. 28 (1997), 1759–1767. (1997) Zbl0877.34006MR1432630
  9. O’Regan D., Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer Academic Publishers, 1997. (1997) Zbl1077.34505MR1449397
  10. Ortega R., Tineo A., Resonance and non-resonance in a problem of boundedness, Proc. Amer. Math. Soc. 124 (1996), 2089–2096. (1996) Zbl0858.34018MR1342038
  11. Volpert V. A., Suhov, Yu. M., Stationary solutions of non-autonomous Kolmogorov-Petrovsky-Piskunov equation, Ergodic Theory Dynam. Systems 19 (1999), 809–835. (1999) MR1695921
  12. Walter W., Differential and Integral Inequalities, Springer-Verlag, Berlin 1970. (1970) Zbl0252.35005MR0271508

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