... critical point of I.Proof. It is obvious that N−∗is closed. Exactly as in the proof of 6, Proposition 3.2, by means of Ekeland’s principle, we derive a PSc2-sequence {un}⊂N−∗ for I. In ... al. 18 for the proof aboutthe decay of positive solution of problem 1.2 which we will use later.Lemma 2.1. Assume a1, f1 and f3 hold. If u ∈ H10Ω is a positive solution of problem ... of problem 1.2,theni u ∈ LqΩ for all q ∈ 2, ∞;ii uy, z → 0 as |z|→0 uniformly for y ∈ ω and u ∈ C1,αΩ for any 0 <α<1;iii for any ∈ 0, 1 μ1, there exist positive...