Nonlinear Eigenvalue Problems for the Dirichlet (p,2)-Laplacian - Yunru Bai; Leszek Gasiński; Nikolaos S. Papageorgiou (Axioms, 2022)
We consider a nonlinear eigenvalue problem driven by the Dirichlet <semantics>(p,2)</semantics>-Laplacian. The parametric reaction is a Carathéodory function which exhibits <semantics>(p−1)</semantics>-sublinear growth as <semantics>x→+∞</semantics> and as <semantics>x→0+</semantics>. Using variational tools and truncation and comparison techniques, we prove a bifurcation-type theorem describing the “spectrum” as <semantics>λ>0</semantics> varies. We also prove the existence of a smallest positive eigenfunction for every eigenvalue. Finally, we indicate how the result can be extended to <semantics>(p,q)</semantics>-equations (<semantics>q≠2</semantics>).