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- W2562509235 abstract "Abstract We consider the system of difference equations $Deltabigg{(}frac{Delta u_{n-1}}{sqrt{1-|Delta u_{n-1}|^{2}}}bigg{)}=% nabla V_{n}(u_{n})+h_{n},quad u_{n}=u_{n+T}quad(ninmathbb{Z}),$ with ${Delta u_{n}=u_{n+1}-u_{n}in{mathbb{R}}^{N}}$ , ${V_{n}=V_{n}(x)in C^{2}({mathbb{R}}^{N},mathbb{R})}$ , ${V_{n+T}=V_{n}}$ , ${h_{n+T}=h_{n}}$ for all ${ninmathbb{Z}}$ and some positive integer T , ${V_{n}(x)}$ is ${omega_{i}}$ -periodic ( ${omega_{i}>0}$ ) with respect to each ${x_{i}}$ ( ${i=1,ldots,N}$ ) and ${sum_{j=1}^{T}h_{j}=0}$ . Applying a modification argument to the corresponding problem with a left-hand member of p -Laplacian type, and using Morse theory, we prove that if all its solutions are non-degenerate, then the difference system above has at least ${2^{N}}$ geometrically distinct T -periodic solutions." @default.
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- W2562509235 date "2017-03-01" @default.
- W2562509235 modified "2023-10-17" @default.
- W2562509235 title "Morse theory and multiple periodic solutions of some quasilinear difference systems with periodic nonlinearities" @default.
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- W2562509235 doi "https://doi.org/10.1515/gmj-2016-0075" @default.
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