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}, pages = {103--128}, publisher = {Elsevier}, volume = {31}, number = {1}, year = {2014}, doi = {10.1016/j.anihpc.2013.02.003}, mrnumber = {3165281}, zbl = {1290.35049}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.003/} }
TY - JOUR AU - Bolotin, Sergey AU - Rabinowitz, Paul H. TI - Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 103 EP - 128 VL - 31 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.003/ DO - 10.1016/j.anihpc.2013.02.003 LA - en ID - AIHPC_2014__31_1_103_0 ER -
%0 Journal Article %A Bolotin, Sergey %A Rabinowitz, Paul H. %T Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 103-128 %V 31 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.003/ %R 10.1016/j.anihpc.2013.02.003 %G en %F 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/articles/10.1016/j.anihpc.2013.02.003/
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