On a nonhomogeneous, nonlinear Dirichlet eigenvalue problem

Zhenhai Liu and Nikolaos S. Papageorgiou

Mathematische Nachrichten, 2023, vol. 296, issue 9, 3986-4001

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).

Date: 2023
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https://doi.org/10.1002/mana.202200040

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