Existence of multi-bump solutions to biharmonic operator with critical exponential growth in ℝ⁴

2016/03/18 by Alânnio B. Nóbrega, Nóbrega, Alânnio B., Denilson S. Pereira +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1603.05946

openalex publication_date 2016/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using variational methods, we establish existence of multi-bump solutions for the following class of problems \ Δ² u +(λV(x)+1)u = f(u), in ℝ⁴, u ∈ H²(ℝ⁴), . where Δ² is the biharmonic operator, f is a continuous function with critical exponential growth and V : ℝ⁴ → ℝ is a continuous function verifying some conditions.

Citations

• Existence of multi-bump solutions for a class of elliptic problems\n involving the biharmonic operator

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