ABSTRACT
Introduction. In this peper, we intend to establish one new result and extend two previous results [3, Thms, 1 & 2], for second order quasilinear elliptic partial differential equations defined on the N-torus. The main point of the extension is that now the leading order coefficienta a ij (x, u) are allowed to have also a linear growth condition with respect to u, i.e. |a ij (x,u) | ≤ a(x) + η|u| vhere a(x) ∈ L 2 (Ω) and η is a positive constant. Here, Ω = {x: -π < x j ≤ π, j = 1,…, N} is the N-torus, N ≥ 2.
