Normalized solutions and stability for biharmonic Schrödinger equation with potential on waveguide manifold

2024/09/20 by Wang, Jun, Yin, Zhaoyang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.00032

Abstract

In this paper, we study the following biharmonic Schrödinger equation with potential and mixed nonlinearities \Δ² u +V(x,y)u+λu =μ|u|^p-2u+|u|^q-2u, (x, y) ∈ Ω_r × \mathbbTⁿ,
∫_Ω_r×\mathbbTⁿu²dxdy=Θ, . where Ω_r ⊂ ℝ^d is an open bounded convex domain, r>0 is large and μ∈ℝ. The exponents satisfy 2

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