On nonlinear boundary value problem corresponding to N-dimensional inverse spectral problem

2018/03/05 by Y.Sh. Ilyasov, Ilyasov, Y. Sh., Н. Ф. Валеев +1 · 1 citation
Mathematics · #35J10 #35J60 #35J65 #35P30 #35R30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1803.01495

openalex publication_date 2018/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a relationship between an inverse optimization spectral problem for N-dimensional Schrödinger equation -Δψ+qψ=λψ and a solution of the nonlinear boundary value problem -Δu+q₀ u=λu- u^γ-1,~~u>0,~~ u|_{∂ Ω}=0. Using this relationship, we find an exact solution for the inverse optimization spectral problem, investigate its stability and obtain new results on the existence and uniqueness of the solution for the nonlinear boundary value problem.

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