Elementary variational approach to zero-free solutions of a nonlinear eigenvalue problem

DOI10.1016/j.na.2007.08.070zbMath1167.47054OpenAlexW2076437788MaRDI QIDQ949732

Gen-Qiang Wang, Sui-Sun Cheng

Publication date: 21 October 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.08.070

zbMATH Keywords

nonlinear eigenvalue problemsubquadratic nonlinearitieselementary variational methodssuperquadratic nonlinearitieszero-free solution

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational principles in infinite-dimensional spaces (58E30) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10)

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• Existence and localization theorems for a discrete nonlinear eigenvalue problem
• Existence of \(2^n\) nontrivial solutions for discrete two-point boundary value problems
• Multiple positive solutions of singular and nonsingular discrete problems via variational methods
• Existence of solutions for a nonlinear system with a parameter
• Periodic solutions of higher-dimensional discrete systems

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