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A system with weights and with critical Sobolev exponent

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Abstract

We investigate the minimization problem

where \(q=\frac{2N}{N-2}\), \( N \geqslant 4\), a and b are two continuous positive weight functions. We show the existence of solutions of the previous minimizing problem under some conditions on a, b, the dimension of the space and the parameter \(\lambda \).

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Authors and Affiliations

  1. Faculty of sciences of Tunis, Department of Mathematics, University of Tunis El Manar, Tunis, Tunisia

    Asma Benhamida

  2. Univ Paris Est Creteil, CNRS, LAMA, 94010, Creteil, France

    Rejeb Hadiji

  3. Univ Gustave Eiffel, LAMA, 77447, Marne-la-Vallée, France

    Rejeb Hadiji

Authors
  1. Asma Benhamida
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  2. Rejeb Hadiji
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Correspondence to Rejeb Hadiji.

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Benhamida, A., Hadiji, R. A system with weights and with critical Sobolev exponent. European Journal of Mathematics 9, 54 (2023). https://doi.org/10.1007/s40879-023-00650-z

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  • DOI: https://doi.org/10.1007/s40879-023-00650-z

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