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    Existence of solutions for fourth order elliptic equations of Kirchhoff type
    (Academic Press Inc Elsevier Science, 2014) Wang, Fanglei; Avci, Mustafa; An, Yukun
    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.