A complete classification of bifurcation diagrams of a p-Laplacian Dirichlet problem

We study the bifurcation diagrams of classical positive solutions u with parallel to u parallel to(infinity) epsilon (0,infinity) of the p-Laplacian Dirichlet problem {(phi(p)(mu'(x)))'+ lambda f(q) (u(X))=0' -1 < X <1, {u(- 1) = 0 = u (1), where p > 1, phi(p) (y) = vertical bar y vertical bar p(-2)y, (phi(p) (u'))' is the one-dimensional p-Laplacian, lambda > 0 is a bifurcation parameter, and f(q) (u) = vertical bar 1 - u vertical bar(q) is defined on [0, infinity) with q > 0. More precisely, for different (p, q), we give a complete classification of bifurcation diagrams of classical positive solutions on the (lambda, parallel to u parallel to(infinity))-plane. Hence we are able to determine the exact multiplicity of classical positive solutions for each (p, q, (c) 2006 Elsevier Inc. All rights reserved.