Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities

2024/10/08 by Bieganowski, Bartosz, Miyagaki, Olímpio Hiroshi, Schino, Jacopo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.05885

Abstract

Via a constrained minimization, we find a solution (λ,u) to the problem \begincases (-Δ)^m u+\fracμ|x|^2mu + λu = ηu³ + g(u)
∫_ℝ^2m u² dx = ρ\endcases with 1 ≤ m ∈ ℕ, μ,η≥ 0, ρ> 0, and g having exponential critical growth at infinity and mass supercritical growth at zero.

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