Multiple critical points in closed sets via minimax theorems

2024/11/06 by Biagio Ricceri, Ricceri, Biagio · 1 citation
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fuzzy Systems and Optimization #Optimization and Mathematical Programming #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2411.03703

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we apply our minimax theory ([4], [5], [6]) with the one developed by A. Moameni in [2] to formalize a general scheme giving the multiplicity of critical points. Here is a sample of application of the scheme to a critical elliptic problem: Let Ω⊂ \bf Rⁿ (n≥ 3) be a smooth bounded domain and let 10, there exists λ^*>0 with the following property: for every λ∈ ]0,λ^*[, μ∈ ]-λ^*,λ^*[, and for every convex dense set S⊂ H^-1(Ω), there exists φ∈ S, with ‖φ‖_H^-1(Ω)

Cited by

• A note on nonlocal discrete problems involving sign-changing Kirchhoff functions

Related

• On the critical points of solutions of PDE in a non-convex settings: the case of concentrating solutions
• Multiplicity of strong solutions for a class of elliptic problems without the Ambrosetti-Rabinowitz condition in ℝ^N
• Multiplicity results for critical p-Laplacian problems
• Multiplicity results for elliptic problems with super-critical concave and convex nonlinearties
• Positive solutions to multi-critical elliptic problems