Published online by Cambridge University Press: 14 November 2011
For the non-linear problem
where f is a discontinuous function at 1, we show that the number of non-trivial positive solutions, for a given real number λ≧0, is related to the graph of a continuous function g. Then, by studying the function g it is possible in some special cases to give, for any λ≧0, the minimal or exact number of non-trivial positive solutions.