A Pohožaev minimization for normalized solutions: fractional sublinear equations of logarithmic type

2025/03/31 by Marco Gallo, Gallo, Marco, Jacopo Schino +1 · 1 citation
Mathematics · #35B06 #35B09 #35B38 #35D30 #35J20 #35Q40 #35Q55 #35R09 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.24080

openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we search for normalized solutions to a fractional, nonlinear, and possibly strongly sublinear Schrödinger equation (-Δ)^s u + μu = g(u) \hboxin ℝ^N, under the mass constraint ∫_ℝ^N u² dx = m>0; here, N≥ 2, s ∈ (0,1), and μ is a Lagrange multiplier. We study the case of L²-subcritical nonlinearities g of Berestycki--Lions type, without assuming that g is superlinear at the origin, which allows us to include examples like a logarithmic term g(u)= ulog(u²) or sublinear powers g(u)=u^q-u^r, 0

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