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 The aim of this paper is to provide the first application of Theorem 3 of [2] in a case where the dependence of the underlying equation from the real parameter is not of affine type. The simplest particular case of our result reads as follows:
Let  be a non-zero continuous function such that 
 where 
Moreover, let  
be two continuous and non-decreasing functions, with k(t) > 0 for all t > 0 and

Then, for each μ large enough, there exist an open interval the problem has at least three solutions whose norms in are less than ρ.

Key words and phrases. Nonlocal problem, multiplicity of solutions, minimax inequality.