Some existence results for a quasilinear problem with source term in Zygmund-space

摘要

In this paper we study the existence of solution to the problem where ? is an open bounded set of R~2, A(x) a coercive matrix with coefficients in L~∞(?), H(x, s, ξ) a Carathéodory function satisfying, for some γ > 0, Here f belongs to L~1 (log L~1)(?) and a_0≥0 to L~q(?), q > 1. For f and a_0 sufficiently small, we prove the existence of at least one solution u of this problem which is such that e~(δ_0|u|) - 1 belongs to H_0~1 (?) for some δ_0≥γ and satisfies an a priori estimate.