Abstract
We study the exact structure of positive solutions of an Ambrosetti-Brezis-Cerami problem and its generalization in one space variable and in the classical Laplacian case. We prove the exact multiplicity result when λλ ranges over the whole interval (0,∞)(0,∞) and get more detailed results of the solution curve. The proof of our exact multiplicity result uses the modified time-map techniques which can be adapted, and the exact multiplicity result can be extended to a more general kk-Laplacian problem with k>1.