Existence and multiplicity results for a second-order multi-point boundary value problem at resonance
- CHEN Bin, Abuelgasimalshaby Elzebir
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(4):
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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)=∑mk=1aku(ηk)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<…<ηm<1, ak>0(k=1,2,…,m).