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On a nonhomogeneous, nonlinear Dirichlet eigenvalue problem

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  • Zhenhai Liu
  • Nikolaos S. Papageorgiou

Abstract

We consider a nonlinear eigenvalue problem for the Dirichlet (p,q)$(p,q)$‐Laplacian with a sign‐changing Carathé$\acute{\rm e}$odory reaction. Using variational tools, truncation and comparison techniques, and critical groups, we prove an existence and multiplicity result which is global in the parameter λ>0$\lambda >0$ (bifurcation‐type theorem). Our work here complements the recent one by Papageorgiou–Qin–Rădulescu, Bull. Sci. Math. 172 (2021).

Suggested Citation

  • Zhenhai Liu & Nikolaos S. Papageorgiou, 2023. "On a nonhomogeneous, nonlinear Dirichlet eigenvalue problem," Mathematische Nachrichten, Wiley Blackwell, vol. 296(9), pages 3986-4001, September.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:9:p:3986-4001
    DOI: 10.1002/mana.202200040
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