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http://dx.doi.org/10.4134/BKMS.b160338

INFINITELY MANY SOLUTIONS FOR A CLASS OF MODIFIED NONLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS ON ℝN  

Che, Guofeng (School of Mathematics and Statistics Central South University)
Chen, Haibo (School of Mathematics and Statistics Central South University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 895-909 More about this Journal
Abstract
This paper is concerned with the following fourth-order elliptic equations $${\Delta}^2u-{\Delta}u+V(x)u-{\frac{k}{2}}{\Delta}(u^2)u=f(x,u),\text{ in }{\mathbb{R}}^N$$, where $N{\leq}6$, ${\kappa}{\geq}0$. Under some appropriate assumptions on V(x) and f(x, u), we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are extended.
Keywords
fourth-order elliptic equations; sublinear; nontrivial solutions; genus theory;
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