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… Click to show full abstract
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).
Keywords:
dirichlet laplacian;
problems dirichlet;
eigenvalue problems;
nonlinear eigenvalue
Journal Title: Axioms
Year Published: 2022
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Journal Title: Axioms
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!