关键词: p-Laplace方程, 正径向解, 变号权, 分歧

Abstract: We investigated the global structure of positive radial solutions for a class of quasilinear elliptic boundary value problems with Dirichlet boundary conditions based on  bifurcation theory. Specifically, by introducing two critical exponents f₀ and f_∞,  under two typical cases of  f₀∈(0,∞), f_∞=0 and f₀=∞, f_∞=0, we prove the existence of unbounded connected branches emanating from bifurcation points, which utimately asymptotically extend to infinity along the λ-axis.

Key words: p-Laplacian equation, positive radial solution, sign-changing weight, bifurcation