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2 results

  • Positive Solutions for the Generalized Nonlinear Logistic Equations

  • Leszek Gasiński, Nikolaos S. Papageorgiou
  • Journal:
    Canadian Mathematical Bulletin / Volume 59 / Issue 1 / 01 March 2016
    Published online by Cambridge University Press:
    20 November 2018, pp. 73-86
    Print publication:
    01 March 2016
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  • We consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiffusive type. Using variational methods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.

  • Three non-trivial solutions for not necessarily coercive p-Laplacian equations

  • Part of
  • Shouchuan Hu, Nikolas S. Papageorgiou
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 3 / October 2009
    Published online by Cambridge University Press:
    23 September 2009, pp. 679-688
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  • We consider the existence of three non-trivial smooth solutions for nonlinear elliptic problems driven by the p-Laplacian. Using variational arguments, coupled with the method of upper and lower solutions, critical groups and suitable truncation techniques, we produce three non-trivial smooth solutions, two of which have constant sign. The hypotheses incorporate both coercive and non-coercive problems in our framework of analysis.