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MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATION VIA VARIATIONAL METHODS

Part of: Boundary value problems

Published online by Cambridge University Press:  13 October 2010

JUNTAO SUN ,
HAIBO CHEN  and
TIEJUN ZHOU
JUNTAO SUN
Affiliation:
Department of Mathematics, Central South University, Changsha, 410075 Hunan, PR China (email: [email protected])
HAIBO CHEN*
Affiliation:
Department of Mathematics, Central South University, Changsha, 410075 Hunan, PR China (email: [email protected])
TIEJUN ZHOU
Affiliation:
College of Science, Hunan Agricultural University, Changsha, 410128, Hunan, PR China (email: [email protected])
*
✉For correspondence; e-mail: math˙[email protected]
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Abstract

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In this paper, we deal with the multiplicity of solutions for a fourth-order impulsive differential equation with a parameter. Using variational methods and a ‘three critical points’ theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. An example is also given in order to illustrate the main results.

Keywords

impulsive differential equationboundary value problemcritical pointsvariational methods

MSC classification

Secondary: 34B15: Nonlinear boundary value problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 3 , December 2010 , pp. 446 - 458
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The first author was supported by the Graduate Degree Thesis Innovation Foundation of Central South University (CX2009B023). The second author was supported by NFSC (10871206).

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