Adams’ type inequality and application to a quasilinear nonhomogeneous equation with singular and vanishing radial potentials in \( \mathbb {R}^4 \)

  • Sami Aouaoui
  • Francisco S. B. Albuquerque


In this paper, we establish some Adams’ type inequality for weighted second-order Sobolev spaces in four dimensions. The weights are radial and can have a singular or decaying behavior. This inequality is used to study some nonhomogeneous quasilinear elliptic equation.


Adams’ inequality Singular or decaying weights Radial functions Nonhomogeneous quasilinear elliptic equation Exponential critical growth 

Mathematics Subject Classification

35A23 35B33 35J30 35J35 35J91 



The authors are very grateful to the anonymous referee for his(her) careful reading of the manuscript and his(her) insightful and constructive remarks and comments that helped to clarify the content and improve the presentation of the results in this paper. The second author is supported by Programa de Incentivo à Pós-Graduacão e Pesquisa(PROPESQ) Edital 2015, UEPB.


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut Supérieur des Mathématiques Appliquées et de l’Informatique de KairouanKairouanTunisia
  2. 2.Departamento de MatemáticaUniversidade Estadual da ParaíbaCampina GrandeBrazil

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