JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 37-41.doi: 10.6040/j.issn.1671-9352.0.2015.385

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Existence of solutions for second-order discrete Neumann problems at resonance

SU Yan   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2015-08-04 Online:2016-06-20 Published:2016-06-15

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Abstract: We consider the existence of solutions for the following nonlinear second order discrete Neumann problem at resonance{Δ2u(t-1)=f(t,u(t),Δu(t)), t∈［1,T］Z,Δu(0)=0, Δu(T)=0,where t∈［1,T］Z={1,2,…,T}, f:［1,T］Z×R2→R is continuous, T≥2 and T∈Z. The methods of lower and upper solutions are developed for the problem by using the connectivity properties of the solution sets of parameterized families of compact vector fields.

Key words: connected sets, Neumann problem, existence, at resonance

CLC Number: 

  • O175.8
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