In:
Boundary Value Problems, Springer Science and Business Media LLC, Vol. 2020, No. 1 ( 2020-12)
Abstract:
This paper is concerned with the following nonlocal fourth-order elliptic problem: $$\begin{aligned} \textstyle\begin{cases} \Delta ^{2}u-m(\int _{\varOmega } \vert \nabla u \vert ^{2} \,dx)\Delta u=a(x) \vert u \vert ^{s-2}u+f(x,u), \quad x\in \varOmega , \\ u=\Delta u=0,\quad x\in \partial \varOmega , \end{cases}\displaystyle \end{aligned}$$ { Δ 2 u − m ( ∫ Ω | ∇ u | 2 d x ) Δ u = a ( x ) | u | s − 2 u + f ( x , u ) , x ∈ Ω , u = Δ u = 0 , x ∈ ∂ Ω , by using the mountain pass theorem, the least action principle, and the Ekeland variational principle, the existence and multiplicity results are obtained.
Type of Medium:
Online Resource
ISSN:
1687-2770
DOI:
10.1186/s13661-020-01430-4
Language:
English
Publisher:
Springer Science and Business Media LLC
Publication Date:
2020
detail.hit.zdb_id:
2187777-4
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