MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

doi:10.1016/S0252-9602(15)30040-0

Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (5): 1067-1076.doi: 10.1016/S0252-9602(15)30040-0

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MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

Liping XU¹, Haibo CHEN²

1. Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China;
2. School of Mathematics and Statistics, Central South University, Changsha 410075, China

Received:2014-01-17 Revised:2015-05-07 Online:2015-09-01 Published:2015-09-01
Contact: Haibo CHEN E-mail:math_chb@csu.edu.cn
Supported by:
This work was supported by Natural Science Foundation of China (11271372) and Hunan Provincial Natural Science Foundation of China (12JJ2004).

Abstract

Abstract:

In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type
???11???
where a,b>0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti-Rabinowitz type condition.

Key words: fourth order elliptic equations of Kirchhoff type, symmetric mountain pass theorem, variational methods

CLC Number:

35J20

Liping XU, Haibo CHEN. MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE[J].Acta mathematica scientia,Series B, 2015, 35(5): 1067-1076.

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MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

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