共振条件下的二阶多点边值问题解的存在性和多解性

doi:10.6040/j.issn.1671-9352.0.2015.308

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 49-52.doi: 10.6040/j.issn.1671-9352.0.2015.308

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Existence and multiplicity results for a second-order multi-point boundary value problem at resonance

CHEN Bin, Abuelgasimalshaby Elzebir

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2015-06-29 Online:2016-04-20 Published:2016-04-08

Abstract

Abstract: It is investigated that the existence and multiplicity results for a second-order multi-point boundary value problem at resonanceu″(t)=f(t,u(t))+e(t), t∈［0,1］,u'(0)=0, u(1)=∑^m_k=1a_ku(η_k)by the connectivity properties of solution set of parameterized families of compact vector fields. where f:［0,1］×R→R is continuous, e∈C(［0,1］,R), 0<η₁<η₂<…<η_m<1, a_k>0(k=1,2,…,m).

Key words: existence of solutions, multiplicity results, at resonance, connectivity properties of solution set, multi-point boundary value problem

CLC Number:

O175.8

CHEN Bin, Abuelgasimalshaby Elzebir. Existence and multiplicity results for a second-order multi-point boundary value problem at resonance[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 49-52.

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