Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 1, p. 103-128
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Variational gluing arguments are employed to construct new families of solutions for a class of semilinear elliptic PDEs. The main tools are the use of invariant regions for an associated heat flow and variational arguments. The latter provide a characterization of critical values of an associated functional. Among the novelties of the paper are the construction of “hybrid” solutions by gluing minima and mountain pass solutions and an analysis of the asymptotics of the gluing process.

@article{AIHPC_2014__31_1_103_0,
     author = {Bolotin, Sergey and Rabinowitz, Paul H.},
     title = {Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {1},
     year = {2014},
     pages = {103-128},
     doi = {10.1016/j.anihpc.2013.02.003},
     zbl = {1290.35049},
     mrnumber = {3165281},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_1_103_0}
}
Bolotin, Sergey; Rabinowitz, Paul H. Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 1, pp. 103-128. doi : 10.1016/j.anihpc.2013.02.003. http://www.numdam.org/item/AIHPC_2014__31_1_103_0/

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