Abstract
We consider positive solutions of a class of semilinear problems u'' + λa(x)f(u) = 0, \qquad −1 < x < 1,\qquad u(−1) = u(1) = 0, with even and positive a(x) , depending on a positive parameter λ . In case f(u) is convex, an exact multiplicity result was given in P. Korman, Y. Li and T. Ouyang [6]; see also P. Korman [4] for the details. It was observed by P. Korman and J. Shi [7] that convexity requirement can be relaxed for large u (see also [5]). We show that convexity requirement can also be relaxed for small u .
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