Infinitely many solutions of elliptic problems with perturbed symmetries in symmetric domains. (English) Zbl 1229.35045

Summary: We study superlinear elliptic boundary value problems with perturbed symmetries in domains which are invariant under the action of a group \(G\). We give conditions on the growth of the nonlinearity which guarantee the existence of infinitely many \(G\)-invariant solutions. These conditions improve those obtained by A. Bahri and P. L. Lions [Commun. Pure Appl. Math. 41, No. 8, 1027–1037 (1988; Zbl 0645.58013)] and P. Bolle, N. Ghoussoub and H. Tehrani [Manuscr. Math. 101, No. 3, 325–350 (2000; Zbl 0963.35001)] if the domain contains a \(G\)-orbit of large enough dimension.


35J20 Variational methods for second-order elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
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