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Gluing approximate solutions of minimum type on the Nehari manifold. (English) Zbl 0963.35052

Summary: In the last decade or so, variational gluing methods have been widely used to construct homoclinic and heteroclinic type solutions of nonlinear elliptic equations and Hamiltonian systems. This note is concerned with the procedure of gluing mountain-pass type solutions. The first procedure to glue mountain-pass type solutions was developed through the work of Sere and Coti Zelati-Rabinowitz. This procedure and its variants have been extensively used in many problems by now for nonlinear equations with superlinear nonlinearities. In this note we provide an alternative device to the by now standard procedure which allows us to glue minimizers on the Nehari manifold together as genuine, multi-bump type, solutions.

MSC:

35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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