| Title:
|
Heteroclinic orbits in plane dynamical systems (English) |
| Author:
|
Malaguti, Luisa |
| Author:
|
Marcelli, Cristina |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
183-200 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
nonlinear boundary value problems |
| Keyword:
|
heteroclinic solutions |
| Keyword:
|
lower and upper solutions |
| Keyword:
|
singular boundary value problems |
| MSC:
|
34B15 |
| MSC:
|
34B16 |
| MSC:
|
34B40 |
| MSC:
|
34C37 |
| MSC:
|
37C29 |
| idZBL:
|
Zbl 1090.34037 |
| idMR:
|
MR1921590 |
| . |
| Date available:
|
2008-06-06T22:30:23Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107832 |
| . |
| Reference:
|
[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. Zbl 0917.34052, MR 1654427 |
| Reference:
|
[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. Zbl 0684.34071, MR 1010959 |
| Reference:
|
[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. Zbl 0954.34029, MR 1765570 |
| Reference:
|
[4] Huang W.: Monotonicity of heteroclinic orbits and spectral properties of variational equations for delay differential equations.J. Differential Equations 162 (2000), 91–139. Zbl 0954.34071, MR 1741874 |
| Reference:
|
[5] Erbe L., Tang M.: Structure of positive radial solutions of semilinear elliptic equations.J. Differential Equations 133 (1997), 179–202. Zbl 0871.34023, MR 1427849 |
| Reference:
|
[6] Malaguti L., Marcelli C.: Existence of bounded trajectories via upper and lower solutions.Discrete Contin. Dynam. Systems 6 (2000), 575–590. Zbl 0979.34019, MR 1757388 |
| Reference:
|
[7] Malaguti L., Marcelli C.: Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms.Math. Nachr. 242 (2002). Zbl 1016.35036, MR 1916855 |
| Reference:
|
[8] Marcelli C., Rubbioni P.: A new extension of classical Müller’s theorem.Nonlinear Anal. 28 (1997), 1759–1767. Zbl 0877.34006, MR 1432630 |
| Reference:
|
[9] O’Regan D.: Existence Theory for Nonlinear Ordinary Differential Equations.Kluwer Academic Publishers, 1997. Zbl 1077.34505, MR 1449397 |
| Reference:
|
[10] Ortega R., Tineo A.: Resonance and non-resonance in a problem of boundedness.Proc. Amer. Math. Soc. 124 (1996), 2089–2096. Zbl 0858.34018, MR 1342038 |
| Reference:
|
[11] Volpert V. A., Suhov, Yu. M.: Stationary solutions of non-autonomous Kolmogorov-Petrovsky-Piskunov equation.Ergodic Theory Dynam. Systems 19 (1999), 809–835. MR 1695921 |
| Reference:
|
[12] Walter W.: Differential and Integral Inequalities.Springer-Verlag, Berlin 1970. Zbl 0252.35005, MR 0271508 |
| . |
