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A generalization of a criterion for the existence of solutions to semilinear elliptic equations

1 Pierre Baras died on April 22nd, 2020. He was still working on a final version of this article but unfortunately could not submit it. This version is essentially the first one he submitted, except for a few technical corrections made with the help of the referee. We would like to express our sincere thanks to the referee for his fruitful help, as well as to "Maha Daoud" who kindly rebuilt the latex source from the pdf submission.
A brief tribute describing some of Pierre Baras' actions may be found just after the preface. The Guest Editors.

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