Infinitely many solutions for Kirchhoff equations with indefinite potential

2023/01/10 by Shuai Jiang, Jiang, Shuai, Shibo Liu +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2301.04236

openalex publication_date 2023/01/10 · openalex created_date 2023/02/15 · openalex updated_date 2026/07/28

Abstract

We obtain a sequence of solutions converging to zero for the Kirchhoff equation -( 1+∫_Ω\vert ∇ u\vert²) Δu+V(x)u=f(u),\qquadu∈ H₀¹(Ω) via truncating technique and a variant of Clark's theorem due to Liu--Wang, where Ω is a bounded smooth domain Ω⊂ℝ^N. Similar result for Schrödinger-Poisson system on a bounded smooth domain Ω⊂ℝ³ is also presented.

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