Abstract
We study the bifurcation curve of (sign-changing and nonnegative) solutions of the boundary blow-up problem (chemical equation presented) where p > 1, ψ <sub>p</sub> (y) = |y| <sup>p-2</sup> y and (ψ <sub>p</sub> (u′))′ is the one-dimensional p-Laplacian, λ > 0, and (chemical equation presented). We give a simple explicit formula of the bifurcation curve of solutions. Thus we are able to determine the shape of the bifurcation curve and hence the exact multiplicity of solutions for any λ > 0. Moreover, when b = a > p - 1 > 0, k = 1, and f <sub>a,b</sub> (u) = -|u| <sup>a</sup> , we investigate the variation of the bifurcation curves with respect to the exponent a.