Multiplicity results for an inhomogeneous Neumann problem with critical exponent (Q1315075)

The author considers the Neumann problem in dimension \(N \geq 5\) \[ - \Delta u + \lambda u = |u |^{p - 2} u + f \text{ in } \Omega, \quad \partial u/ \partial n = 0 \text{ on } \partial \Omega, \] where \(\Omega \subset \mathbb{R}^N\) is a bounded domain, \(\lambda > 0\) and \(p = 2N/(N - 2)\) is the critical exponent for the Sobolev embedding. The main result states the existence of at least three solutions if \(f \not \equiv 0\) satisfies a certain ``smallness'' condition. The proof uses essentially the same approach as in the author's previous paper [Ann. Inst. Henri Poincaré, Anal. Nonlinéaire 9, No. 3, 281-304 (1992; Zbl 0785.35046)].