Nonlinear Eigenvalue Problems for the Dirichlet (p, 2)-Laplacian

作者：Yunru Bai, L. Gasiński, N. Papageorgiou · 发表于：Axioms · 年份：2022 · DOI：10.3390/axioms11020058 · 被引用次数：3 · 研究领域：Computer Science

We consider a nonlinear eigenvalue problem driven by the Dirichlet (p,2)-Laplacian. The parametric reaction is a Carathéodory function which exhibits (p−1)-sublinear growth as x→+∞ and as x→0+. Using variational tools and truncation and comparison techniques, we prove a bifurcation-type theorem describing the “spectrum” as λ>0 varies. We also prove the existence of a smallest positive eigenfunction for every eigenvalue. Finally, we indicate how the result can be extended to (p,q)-equations (q≠2).