Bifurcation of sign-changing solutions for one-dimensional p-Laplacian with a strong singular weight: p-superlinear at ∞

We investigate Dirichlet boundary value problems of one-dimensional p-Laplace equations with a singular weight which may not be in L(1). Using the properties of eigenfunctions and the global bifurcation theory and considering the case, p-superlinear at infinity, we obtain the similar results as seen in [1] of the case, p-sublinear at infinity. Moreover, we obtain the existence of sign-changing solutions when the nonlinear term is asymptotically p-sublinear near O and p-superlinear at infinity. (C) 2011 Elsevier Ltd. All rights reserved.