2022/05/03 by Biagio Ricceri, Ricceri, Biagio · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2205.01525
openalex publication_date 2022/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Here is a sample of the results proved in this paper: Let f:\bf R→ \bf R be a continuous function, let ρ>0 and let ω:[0,ρ[→ [0,+∞[ be a continuous increasing function such that limξ→ ρ-∫0ξω(x)dx=+∞. Consider C0([0,1])× C0([0,1]) endowed with the norm ‖(α,β)‖=∫01|α(t)|dt+∫01|β(t)|dt . Then, the following assertions are equivalent: (a) the restriction of f to [-√ρ\over 2,√ρ\over 2 ] is not constant; (b) for every convex set S⊆ C0([0,1])× C0([0,1]) dense in C0([0,1])× C0([0,1]), there exists (α,β)∈ S such that the problem \cases-ω(∫01|u'(t)|2dt)u"=β(t)f(u)+α(t) amp; in [0,1]\cr amp; \cr u(0)=u(1)=0\cr amp; \cr ∫01|u'(t)|2dtlt;ρ\cr has at least two classical solutions.