Multiple solutions for a fourth-order nonlinear elliptic problem which is superlinear at +∞ and linear at −∞

被引：0
作者：
Ruichang Pei
Jihui Zhang
机构：
[1] Tianshui Normal University,School of Mathematics and Statistics
[2] Nanjing Normal University,School of Mathematics and Computer Sciences
来源：
Boundary Value Problems | / 2014卷
关键词：
fourth-order elliptic boundary value problems; multiple solutions; critical groups; Morse theory;
D O I：
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摘要：
We consider a semilinear fourth-order elliptic equation with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and at −∞. Namely, it is linear at −∞ and superlinear at +∞. Combining variational methods with Morse theory, we show that the problem has at least two nontrivial solutions, one of which is negative.
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