Global bifurcation diagrams of positive solutions for a class of 1-D superlinear indefinite problems
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This paper analyzes the structure of the set of positive solutions of a class of one-dimensional symmetric superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its numerical study confirms and illuminates the analysis. On the analytical side, we establish the fast point-wise decay of the positive solutions as λ↓ -∞ in the region where a(x)<0, and solve positively the conjecture of R. Gómez-Reñasco and J. López-Gómez in two special cases of interest, where we show the existence of 2^n+1-1 positive solutions for sufficiently negative λ. On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.
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