MULTIPLE SOLUTIONS FOR A CLASS OF MODIFIED QUASILINEAR FOURTH-ORDER ELLIPTIC EQUATIONS

Zijian Wu; Haibo Chen

doi:10.11948/20210401

2022 Volume 12 Issue 5

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Zijian Wu, Haibo Chen. MULTIPLE SOLUTIONS FOR A CLASS OF MODIFIED QUASILINEAR FOURTH-ORDER ELLIPTIC EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1945-1958. doi: 10.11948/20210401

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Zijian Wu, Haibo Chen. MULTIPLE SOLUTIONS FOR A CLASS OF MODIFIED QUASILINEAR FOURTH-ORDER ELLIPTIC EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1945-1958. doi: 10.11948/20210401

MULTIPLE SOLUTIONS FOR A CLASS OF MODIFIED QUASILINEAR FOURTH-ORDER ELLIPTIC EQUATIONS

Zijian Wu¹,
Haibo Chen^1, ,

1.
School of Mathematics and Statistics, Central South University, Yuelu Street, 410083 Changsha, China

Corresponding author: Email address: math_chb@163.com(H. Chen)

Abstract

Abstract

In this paper, we consider the following modified quasilinear fourth-order elliptic equations:

$ \begin{equation*} \Delta^2u-(a+b\int_{ \mathbb{R}^3}|\nabla u|^2dx)\Delta u+V(x)u-\frac{\kappa}{2}\Delta(u^2)u=f(x, u), \quad \mbox{ in } \mathbb{R}^3, \end{equation*} $

where $ a>0, b\geq0, \kappa\geq0 $. Under some appropriate assumptions on $ V(x) $ and $ f(x, u) $, multiplicity results of two different type of solutions are established via the Mountain Pass lemma and the local minimization.
- Fourth-order elliptic equations /
- multiple solutions /
- Mountain Pass lemma /
- local minimization
MSC: 35J35, 35J62

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References

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