Two solutions for a singular elliptic problem indefinite in sign

  • Giovanni Anello
  • Francesca FaraciEmail author


In this paper we deal with a singular elliptic problem involving a nonlinearity which is indefinite in sign. We prove the existence of two non negative solutions, one of them being positive. The approach relies on suitable truncation methods and variational arguments.

Mathematics Subject Classification

34B16 35J20 


Singular elliptic problem Indefinite nonlinearities Variational methods 


  1. 1.
    Agmon S.: The L p approach to the Dirichlet problem. Ann. Sc. Norm. Sup. Pisa 13, 405–448 (1959)MathSciNetGoogle Scholar
  2. 2.
    Brezis, H., Nirenberg, L.: H 1 versus C 1 local minimizers. C.R. Acad. Sci Paris 317(Sèrie I), 465–472 (1993)Google Scholar
  3. 3.
    Dávila J., Montenegro M.: Positive versus free boundary solutions to a singular elliptic equation. J. Anal. Math. 90, 303–335 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Hernàndez, J., Mancebo, F.J., Vega, J.M.: Positive solutions for singular nonlinear elliptic equations. Proc. R. Soc. Edinb. 137(A), 4162 (2007)Google Scholar
  5. 5.
    Montenegro M., Silva E.: Two solutions for a singular elliptic equation by variational methods. Ann. Sc. Norm. Super. Pisa Cl. Sci. 11, 143–165 (2012)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Pucci P., Serrin J.: A mountain pass theorem. J. Differ. Equ. 60, 142–149 (1985)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Zeidler, E.: Nonlinear Functional Analysis and Its Applications, III, Variational Methods and Optimization. Springer, New York (1985)Google Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di MessinaMessinaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di CataniaCataniaItaly

Personalised recommendations