On the minimal number of critical points of a real function defined on a manifold.

И. Гордон

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On existence of positive solutions for a class of Caffarelli-Kohn-Nirenberg type equations

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We investigate the solvability of a singular equation of Caffarelli-Kohn-Nirenberg type having a critical-like nonlinearity with a sign-changing weight function. We shall examine how the properties of the Nehari manifold and the fibering maps affect the question of existence of positive solutions.