JournalsaihpcVol. 31, No. 1pp. 103–128

Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs

  • Sergey Bolotin

    Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, United States, Steklov Mathematical Institute, Moscow, Russian Federation

  • Paul H. Rabinowitz

    Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, United States
Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs cover
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Abstract

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.

Cite this article

Sergey Bolotin, Paul H. Rabinowitz, Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 1, pp. 103–128

DOI 10.1016/J.ANIHPC.2013.02.003