JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (6): 53-56.doi: 10.6040/j.issn.1671-9352.0.2017.647

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Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points

WANG Su-yun, LI Yong-jun   

  1. School of Mathematics, Lanzhou City University, Lanzhou 730070, Gansu, China
  • Received:2017-12-19 Online:2018-06-20 Published:2018-06-13

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Abstract: We study the existence and uniqueness of solutions of the boundary value problem for nonlinear second-order ordinary equations:{u″+f(t,u)=h(t), t∈(0,1),u(0)=u(1)=0,under the conditions that (f(t,s))/s may exceeds the eigenvalue interval ［λk0, λk0+1］ in some “smaller sets”. The existence and uniqueness of solutions of this equation are obtained.

Key words: second-order boundary value problem, eigenvalue, existence and uniqueness of solutions, contraction mapping principle

CLC Number: 

  • O175.8
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