On “multibump” bound states for certain semilinear elliptic equations. (English) Zbl 0796.35043

Summary: This paper concerns multiplicity results for certain semilinear elliptic equations on \(\mathbb{R}^ N\) with asymptotically periodic structure. In particular, we develop variational methods to construct “multibump” solutions, i.e., solutions with most of their mass lying in widely separated regions. We prove the following result: for each \(k \geq 2\), our asymptotically periodic problem possesses infinitely many \(k\)-bump solutions, provided that the associated periodic problem has only finitely many \(\mathbb{Z}^ N\)-distinct lowest-energy solutions.


35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35B10 Periodic solutions to PDEs
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