Existence of positive solutions for higher order singular sublinear elliptic equations

Abstract

We present existence result for the polyharmonic nonlinear problem (-Δ)pmu = φ(., u) + ψ(., u), in B u > 0, in B lim|x|→1 (-Δ)jmu(x) / (1 - |x|)m-1 = 0, 0 ≤ j ≤ p - 1, in the sense of distributions. Here m, p are positive integers, B is the unit ball in ℝn(n ≥ 2) and the nonlinearity is a sum of a singular and sublinear terms satisfying some appropriate conditions related to a polyharmonic Kato class of functions J(p)m,n.