Nodal solutions for the weighted biharmonic equation with critical exponential growth

2022/06/20 by Brahim Dridi, Dridi, Brahim, Rachaid Jaidane +1
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.10001

openalex publication_date 2022/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we deal with the logarithmic weighted fourth order elliptic equation in the unit disk of B⊂\R⁴: (P_λ)~~Δ(w(x) Δu) = λ f(x,u) in B, u=(∂ u)/(∂ n) on ∂ B, where the nonlinearity f is assumed to have exponential critical growth in view of Adam's type inequalities. By using the constrained minimization in Nehari set combined with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions to the problem (P_λ) .

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