Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients |
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| Authors: | Yuhua Long |
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| Institution: | 1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, People's Republic of China;2. Center for Applied Mathematics, Guangzhou University, Guangzhou, People's Republic of China sxlongyuhua@gzhu.edu.cn longyuhua214@163.com |
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| Abstract: | In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones. |
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| Keywords: | Multiple solutions sign-changing solution invariant sets of descending flow second-order functional difference equation |
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