Ground state solution of a Kirchhoff type equation with singular potentials

2022/12/15 by Thanh Viet Phan, Phan, Thanh Viet
Computer Science · Mathematics · #35Q40 #46N50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2212.07955

openalex publication_date 2022/12/15 · openalex created_date 2022/12/28 · openalex updated_date 2026/07/28

Abstract

We study the existence and blow-up behavior of minimizers for E(b)=inf\E_b(u) | u∈ H¹(R²), ‖u‖_L²=1\, here E_b(u) is the Kirchhoff energy functional defined by E_b(u)= ∫_R² |∇ u|² dx+ b(∫_R² |∇ u|²d x)²+∫_R² V(x) |u(x)|² dx - (a)/(2) ∫_R² |u|⁴ dx, where a>0 and b>0 are constants. When V(x)= -|x|^-p with 0

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