Existence of sign-changing solutions for a logarithmic weighted Kirchhoff problem in the whole of ℝ^N with exponential growth non-linearity

2023/09/19 by Rached Jaidane, Jaidane, Rached
Computer Science · Engineering · Mathematics · #$35$J$20$ #$35$J$30$ #$35$J$60$ #$35$K$57$ #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2309.10768

openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we establish the existence of solutions that change sign at low energy for a non-local weighted Kirchhoff problem in the set ℝ^N, N>2. The non-linearity of the equation is assumed to have exponential growth in view of the logarithmic weighted Trudinger-Moser inequalities. To obtain the existence result, we apply the constrained minimisation in the Nehari set, the quantitative deformation lemma and results from degree theory.

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