Bifurcation for Quasilinear Elliptic Singular BVP

Abstract

For a continuous function g ≥ 0 on (0, + ∞) (which may be singular at zero), we confront a quasilinear elliptic differential operator with natural growth in ∇u, − Δu + g(u)|∇u|2, with a power type nonlinearity, λu p + f 0(x). The range of values of the parameter λ for which the associated homogeneous Dirichlet boundary value problem admits positive solutions depends on the behavior of g and on the exponent p. Using bifurcations techniques we deduce sufficient conditions for the boundedness or unboundedness of the cited range.