Existence and multiplicity of nontrivial solutions for some biharmonic equations with p-Laplacian

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Sun, Juntao^1,2  Chu, Jifeng³  Wu, Tsung-fang⁴ 

[1] Shandong Univ Technol, Sch Sci, Zibo 255049, Peoples R China

[2] Hohai Univ, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China

[3] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[4] Natl Univ Kaohsiung, Dept Appl Math, Kaohsiung 811, Taiwan

关键词: Biharmonic equations;    p-Laplacian;    Variational methods;    Gagliardo-Nirenberg inequality;   

DOI  :  10.1016/j.jde.2016.10.001

来源: Elsevier

【 摘 要 】

We investigate a class of nonlinear biharmonic equations with p-Laplacian {Delta(2)u - beta Delta(p)u + lambda V(x)u = f(x,u) in R-N, u is an element of H-2(R-N), where N >= 1, beta is an element of R, lambda > 0 is a parameter and Delta(p)u = div(|del u|(p-2)Vu) with p >= 2. Unlike most other papers on this problem, we replace Laplacian with p-Laplacian and allow beta to be negative. Under some suitable assumptions on V(x) and f(x, u), we obtain the existence and multiplicity of nontrivial solutions for lambda large enough. The proof is based on variational methods as well as Gagliardo-Nirenberg inequality. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free