A sufficient and necessary condition for one dimensional boundary blow-up problem with p-Laplace operator

Abstract

The existence, uniqueness and asymptotic behavior for one dimensional boundary blow-up problem with p-Laplace operator has been investigated. This problem arises in many fields, such as in the theory of automorphic functions and Riemann surfaces of constant negative curvature, in the study of the electric potential in a glowing hollow metal body, etc. Our result shows that the boundary blow-up solution exists provided that the Keller-Osserman condition holds true and the absorb terms satisfy a divergent condition in some neighbourhood of zero. By symmetry method, comparison theorem and the regularly varying theory, we also investigate the uniqueness of the boundary blow-up solutions, these results can be seen as the beneficial supplement to the corresponding results of elliptic equations.