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Solutions with sign information for nonlinear nonhomogeneous problems

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  • Nikolaos S. Papageorgiou
  • Patrick Winkert

Abstract

We consider a parametric elliptic equation driven by a nonlinear nonhomogeneous differential operator and with a Robin boundary condition. In the first part we prove the existence of positive solutions and state a bifurcation‐type result describing how the set of positive solutions changes as the parameter λ>0 varies. In the second part we show that problem admits nodal (sign‐changing) solutions provided the parameter λ>0 is sufficiently large.

Suggested Citation

  • Nikolaos S. Papageorgiou & Patrick Winkert, 2019. "Solutions with sign information for nonlinear nonhomogeneous problems," Mathematische Nachrichten, Wiley Blackwell, vol. 292(4), pages 871-891, April.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:4:p:871-891
    DOI: 10.1002/mana.201800083
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    Cited by:

    1. Dumitru Motreanu & Angela Sciammetta & Elisabetta Tornatore, 2020. "A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence," Mathematics, MDPI, vol. 8(5), pages 1-13, April.

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