Existence of solutions for fourth order elliptic equations of Kirchhoff type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Wang, Fanglei¹  Avci, Mustafa²  An, Yukun³ 

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

[2] Dicle Univ, Dept Math, Fac Sci, TR-21280 Diyarbakir, Turkey

[3] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

关键词: Fourth order elliptic equation;    Nontrivial solutions;    Mountain pass theorem;    Truncation method;   

DOI  :  10.1016/j.jmaa.2013.07.003

来源: Elsevier

【 摘 要 】

This paper is concerned with the existence of nontrivial solutions for a class of fourth order elliptic equations of Kirchhoff type {Delta 2u - lambda (a + b integral(Omega)vertical bar del u vertical bar(2)dx) Delta u = f(x, u), in Omega, u = 0, Delta u = 0, on partial derivative Omega, where a > 0, b >= 0 are constants, and lambda > 0 is a parameter. We will show that there exists a lambda* such that (1) has nontrivial solutions for 0 < lambda < lambda* by using the mountain pass techniques and the truncation method. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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