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Positive solutions for singular elliptic systems with convection term

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Abstract

We prove the existence and regularity of solutions for a quasi-linear elliptic system with convection terms that can be singular in the solution and its gradient. Comparison properties and a priori estimates are also obtained. Our approach relies on invariance, regularity, strong maximum principle, and fixed-point arguments.

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References

  1. Alves, C.O., Corrêa, F.J.S.A.: On the existence of positive solutions for a class of singular systems involving quasilinear operators. Appl. Math. Comput. 185, 727–736 (2007)

    MathSciNet  MATH  Google Scholar 

  2. Alves, C.O., Corrêa, F.J.S.A., Gonçalves, J.V.A.: Existence of solutions for some classes of singular Hamiltonian systems. Adv. Nonlinear Stud. 5, 265–278 (2005)

    MathSciNet  MATH  Google Scholar 

  3. Alves, C.O., Carrião, P.C., Faria, L.F.O.: Existence of solutions to singular elliptic equations with convection terms via the Galerkin method. Electron. J. Differ. Equations 201012, 12 (2010)

    MathSciNet  MATH  Google Scholar 

  4. Alves, C.O., Moussaoui, A.: Existence of solutions for a class of singular elliptic systems with convection term. Asymptot. Anal. 90, 237–248 (2014)

    MathSciNet  MATH  Google Scholar 

  5. Brézis, H.: Analyse fonctionnelle. Théorie et applications, Masson, Paris (1983)

    MATH  Google Scholar 

  6. Bueno, H., Ercole, G.: A quasilinear problem with fast growing gradient. Appl. Math. Lett. 26, 520–523 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cuesta, M., Takac, P.: Nonlinear eigenvalue problems for degenerate elliptic systems. Differ. Integral Equations 23, 1117–1138 (2010)

    MathSciNet  MATH  Google Scholar 

  8. El Manouni, S., Perera, K., Shivaji, R.: On singular quasimonotone (p, q)-Laplacian systems. Proc. R. Soc. Edinb. Sect. A 142, 585–594 (2012)

    Article  MATH  Google Scholar 

  9. Ghergu, M.: Lane-Emden systems with negative exponents. J. Funct. Anal. 258, 3295–3318 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ghergu, M.: Lane-Emden systems with singular data Proc. R. Soc. Edinburgh Sect. A 141, 1279–1294 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hernández, J., Mancebo, F.J., Vega, J.M.: Positive solutions for singular semilinear elliptic systems. Adv. Differ. Equations 13, 857–880 (2008)

    MathSciNet  MATH  Google Scholar 

  12. Lieberman, G.M.: Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal. 12, 1203–1219 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  13. Montenegro, M., Suarez, A.: Existence of a positive solution for a singular system. Proc. R. Soc. Edinb. Sect. A 140, 435–447 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Motreanu, D., Moussaoui, A.: Existence and boundedness of solutions for a singular cooperative quasilinear elliptic system. Complex Var. Elliptic Equations 59, 285–296 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Motreanu, D., Moussaoui, A.: A quasilinear singular elliptic system without cooperative structure. Acta Math. Sci. 34, 905–916 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Motreanu, D., Moussaoui, A.: An existence result for a class of quasilinear singular competitive elliptic systems. Appl. Math. Lett. 38, 33–37 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Vázquez, J.L.: A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12, 191–202 (1984)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Département de Mathématiques, Université de Perpignan, 66860, Perpignan, France

    Dumitru Motreanu

  2. Biology Department, Mira Bejaia University, Targa Ouzemour, 06000, Bejaïa, Algeria

    Abdelkrim Moussaoui

  3. Academy of Mathematics and Systems Science, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China

    Zhitao Zhang

Authors
  1. Dumitru Motreanu
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  2. Abdelkrim Moussaoui
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  3. Zhitao Zhang
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Correspondence to Dumitru Motreanu.

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Motreanu, D., Moussaoui, A. & Zhang, Z. Positive solutions for singular elliptic systems with convection term. J. Fixed Point Theory Appl. 19, 2165–2175 (2017). https://doi.org/10.1007/s11784-017-0407-3

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  • DOI: https://doi.org/10.1007/s11784-017-0407-3

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