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

We investigate Dirichlet boundary value problems of one-dimensional pp-Laplace equations with a singular weight which may not be in L1L1. Using the properties of eigenfunctions and the global bifurcation theory and considering the case, pp-superlinear at ∞∞, we obtain the similar results as seen in [1] of the case, pp-sublinear at ∞∞. Moreover, we obtain the existence of sign-changing solutions when the nonlinear term is asymptotically pp-sublinear near 00 and pp-superlinear at ∞∞.