Existence of solutions for some discrete boundary value problems with a parameter |
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Authors: | Yang Yang Jihui Zhang |
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Institution: | a School of Science, Jiangnan University, Wuxi, People’s Republic of China b Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing, People’s Republic of China |
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Abstract: | In this paper, the existence and multiplicity results of solutions are obtained for the discrete nonlinear two point boundary value problem (BVP) ; u(0)=0=Δu(T), where T is a positive integer, Z(1,T)={1,2,…,T}, Δ is the forward difference operator defined by Δu(k)=u(k+1)-u(k) and f:Z(1,T)×R→R is continuous, λ∈R+ is a parameter. By using the critical point theory and Morse theory, we obtain that the above (BVP) has solutions for λ being in some different intervals. |
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Keywords: | Discrete Homological nontrivial critical point Morse theory Local linking |
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