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

Volume 120 / 2010

J. Chabrowski, D. G. Costa Colloquium Mathematicum 120 (2010), 43-62 MSC: 35B33, 35J65, 35Q55. DOI: 10.4064/cm120-1-4


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.


  • J. ChabrowskiDepartment of Mathematics
    University of Queensland
    St. Lucia 4072, Qld, Australia
  • D. G. CostaDepartment of Mathematical Sciences
    University of Nevada Las Vegas
    Box 454020
    Las Vegas, NV 89154-4020, U.S.A.

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