Multiple solutions for elliptic resonant problems. (English) Zbl 1155.35354

Liu, Shibo

Proc. R. Soc. Edinb., Sect. A, Math. 138, No. 6, 1281-1289 (2008).

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)

Keywords:

elliptic resonant problems; Lyapunov-Schmidt reduction; critical pints