Multiplicity Result for Quasilinear Elliptic Problems with General Growth in the Gradient

Abstract

Abstract The main result of this work is to get the existence of infinitely many radial positive solutions to the problem -Δpu = |▽u|q + λf(x) in Ω, u|aΩ = 0, where Ω = B1(0) and f is a radial positive function. Since, in general when q ≠ p, a Hopf-Cole type change can not be used, we will consider just the existence and multiplicity of positive radial solutions. The main idea is to get a relation between radial positive solutions of the above equation and a suitable quasilinear family of problems with measures data that we will make precise later.