Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.04.20
  • Published : 2017.05.31
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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.

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References

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