JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 33-39.doi: 10.6040/j.issn.1671-9352.0.2021.428

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Solvability for a class of third-order m-point boundary value problems at resonance with dim Ker L=2

DU Rui-juan   

  1. School of Artificial Intelligence, Gansu University of Political Science and Law, Lanzhou 730070, Gansu, China
  • Published:2021-11-25

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Abstract: The author consider the solvability for a class of third order m-point boundary value problems at resonance with dim Ker L=2{u(t)=f(t,u(t),u'(t),u″(t))+e(t), t∈［0,1］,u(0)=∑m-2i=1αiu(ξi), u(1)=∑n-2j=1βju(ηj), u″(0)=0,where f:［0,1］×R3→R satisfies Carathéodory conditions, e:［0,1］→R∈L1［0,1］, αi,βj∈R,ξi,ηj∈(0,1),0<ξ1<ξ2<…<ξm-2<1,0<η1<η2<…<ηn-2<1, and satisfy the following condition(C1): ∑m-2i=1αi=1,∑m-2i=1αiξi=0,∑βj=1,∑βjηj=1.

Key words: boundary value problem, resonance, Mawhin degree

CLC Number: 

  • O175.8
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