An optimal condition is given for the existence of positive solutions of nonlinear Kirchhoff PDE with strong singularities. A byproduct is that −2 is no longer the critical position for the existence of positive solutions of PDE's with singular potentials and negative powers of the form: −|x| α ∆u = u −γ in Ω, u = 0 on ∂Ω, where Ω is a bounded domain of R N containing 0, with N ≥ 3, α ∈ (0, N ) and −γ ∈ (−3, −1).

It is a customary manipulation for destructive cult to deceive followers under the guise of orthodox religion. Thus, if only to reveal the words and deeds, it is difficult for the dupes to know destructive cult correctly and then break away from it, because understanding the reason for the words and deeds of a man is more important than what he says and does. Based on this, this article puts forward a psychological way to distinguish and recognize orthodox religion and destructive cult: All the motives of the hierarch to create the traditional religion are kind, loving, even noble, and great, while the motives of the hierarch to create destructive cult are to defraud the power to control, deceive sex, and swindle wealth.

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The pseudo religion is widely criticized for its theft and manipulation of dogmata and jargon concepts in orthodox religion to pretend to be orthodox religion and to deceive the public. However it is still in the air to expose its specific content, tactics and purpose stolen and tampered psychologically. This paper discusses the importance of establishment and development of pseudo religion through stealing religious mental concepts in traditional religion including "God", "Heaven", "Hell", "Soul immortality", "Morality" and "Religious feeling", and studies its tricks for theft and manipulation, distortion and ultimate purposes. This paper aims at showing people the evil of pseudo religion and integrity of traditional religion.