Geodesic
Heteroclinic orbits in plane dynamical systems
Archivum mathematicum, Tome 38 (2002) no. 3, pp. 183-200

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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.
Classification : 34B15, 34B16, 34B40, 34C37, 37C29
Keywords: nonlinear boundary value problems; heteroclinic solutions; lower and upper solutions; singular boundary value problems 
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     author = {Malaguti, Luisa and Marcelli, Cristina},
     title = {Heteroclinic orbits in plane dynamical systems},
     journal = {Archivum mathematicum},
     pages = {183--200},
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     volume = {38},
     number = {3},
     year = {2002},
     mrnumber = {1921590},
     zbl = {1090.34037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2002__38_3_a2/}
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Malaguti, Luisa; Marcelli, Cristina. Heteroclinic orbits in plane dynamical systems. Archivum mathematicum, Tome 38 (2002) no. 3, pp. 183-200. http://geodesic.mathdoc.fr/item/ARM_2002__38_3_a2/