一类三阶两点边值问题的变号解

Abstract

Abstract:

In this paper, we use the fixed point index theory and the Leray-Schauder degree theory to discuss the third-order boundary value problem -u'''(t)=f(t, u(t)) for all t ∈[0,1] subject to u(0)=u'(0)=u''(1)=0, where f ∈C([0,1]×R, R). By computing hardly the eigenvalues and their algebraic multiplicities of the associated linear problem, we obtain some new existence results concerning sign-changing solutions to this problem. If f satisfies certain conditions, then the problem has at least six different nontrivial solutions: two positive solutions, two negative solutions and two sign-changing solutions. Moreover, if f(t, •) is odd for all t ∈[0,1], then the problem has at least eight different nontrivial solutions, which are two positive, two negative and four sign-changing solutions.

Key words: Third-order boundary value problem, Sign-changing solutions, Fixed point index, Leray-Schauder degree

CLC Number:

34B15

ZHANG Qi. Sign-changing Solutions to Third-order Two-point Boundary Value Problem[J].Acta mathematica scientia,Series A, 2013, 33(2): 216-223.

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Sign-changing Solutions to Third-order Two-point Boundary Value Problem

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