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

2016/02/09 by Claudianor O. Alves, Alves, Claudianor O., Alânnio B. Nóbrega +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1602.03112

openalex publication_date 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using variational methods, we establish existence of multi-bump solutions for\nthe following class of problems\n \n
left
\n
n
Delta² u +(
lambda V(x)+1)u = f(u),
quad
mboxin
quad
mathbbR^N, u\n
in H²(
mathbbR^N),\n
n
right.\n where N \≥ 1, \Δ² is the biharmonic operator, f is a\ncontinuous function with subcritical growth and V : \ℝ^N \→\n\ℝ is a continuous function verifying some conditions.\n

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