Sign-changing solution for logarithmic elliptic equations with critical exponent

2023/08/17 by Tianhao Liu, Wenming Zou, Liu, Tianhao +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2308.08719

openalex publication_date 2023/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the logarithmic elliptic equations with critical exponent \begincases -Δu=λu+ |u|^{2^*-2}u+θulog u²,
u ∈ H₀¹(Ω), Ω⊂ \R^N. \endcases Here, the parameters N≥ 6, λ∈ \R, θ>0 and 2^*=(2N)/(N-2) is the Sobolev critical exponent. We prove the existence of sign-changing solution with exactly two nodal domain for an arbitrary smooth bounded domain Ω⊂ ℝ^N. When Ω=B_R(0) is a ball, we also construct infinitely many radial sign-changing solutions with alternating signs and prescribed nodal characteristic.

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