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Multiple solutions for elliptic resonant problems. (English) Zbl 1155.35354
Summary: Two non-trivial solutions for semilinear elliptic resonant problems are obtained via the Lyapunov-Schmidt reduction and the three-critical-points theorem. The difficulty that the variational functional does not satisfy the Palais-Smale condition is overcome by taking advantage of the reduction and a careful analysis of the reduced functional.

MSC:
35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
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