Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign
In this article, we are concerned with the periodic solutions of first-order difference equation Δu(t−1)=f(t,u(t))−s,t∈Z,(P)\Delta u\left(t-1)=f\left(t,u\left(t))-s,\hspace{1em}t\in {\mathbb{Z}},\hspace{1.0em}\hspace{1.0em}\left(P) where s∈Rs\in {\mathbb{R}}, f:Z×R→Rf:{\mathbb{Z}}\times {\mathbb{R}}...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-08-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0470 |
| _version_ | 1797998378330619904 |
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| author | Zhao Jiao Ma Ruyun |
| author_facet | Zhao Jiao Ma Ruyun |
| author_sort | Zhao Jiao |
| collection | DOAJ |
| description | In this article, we are concerned with the periodic solutions of first-order difference equation Δu(t−1)=f(t,u(t))−s,t∈Z,(P)\Delta u\left(t-1)=f\left(t,u\left(t))-s,\hspace{1em}t\in {\mathbb{Z}},\hspace{1.0em}\hspace{1.0em}\left(P) where s∈Rs\in {\mathbb{R}}, f:Z×R→Rf:{\mathbb{Z}}\times {\mathbb{R}}\to {\mathbb{R}} is continuous with respect to u∈Ru\in {\mathbb{R}}, f(t,u)=f(t+T,u)f\left(t,u)=f\left(t+T,u), T>1T\gt 1 is an integer, Δu(t−1)=u(t)−u(t−1)\Delta u\left(t-1)=u\left(t)-u\left(t-1). We prove a result of Ambrosetti-Prodi-type for (P)\left(P) by using the method of lower and upper solutions and topological degree. We relax the coercivity assumption on ff in Bereanu and Mawhin [1] and obtain Ambrosetti-Prodi-type results. |
| first_indexed | 2024-04-11T10:47:47Z |
| format | Article |
| id | doaj.art-90374de255e44c2caa30fdf723714e8d |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-11T10:47:47Z |
| publishDate | 2022-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-90374de255e44c2caa30fdf723714e8d2022-12-22T04:29:00ZengDe GruyterOpen Mathematics2391-54552022-08-0120178379010.1515/math-2022-0470Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in signZhao Jiao0Ma Ruyun1Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. ChinaIn this article, we are concerned with the periodic solutions of first-order difference equation Δu(t−1)=f(t,u(t))−s,t∈Z,(P)\Delta u\left(t-1)=f\left(t,u\left(t))-s,\hspace{1em}t\in {\mathbb{Z}},\hspace{1.0em}\hspace{1.0em}\left(P) where s∈Rs\in {\mathbb{R}}, f:Z×R→Rf:{\mathbb{Z}}\times {\mathbb{R}}\to {\mathbb{R}} is continuous with respect to u∈Ru\in {\mathbb{R}}, f(t,u)=f(t+T,u)f\left(t,u)=f\left(t+T,u), T>1T\gt 1 is an integer, Δu(t−1)=u(t)−u(t−1)\Delta u\left(t-1)=u\left(t)-u\left(t-1). We prove a result of Ambrosetti-Prodi-type for (P)\left(P) by using the method of lower and upper solutions and topological degree. We relax the coercivity assumption on ff in Bereanu and Mawhin [1] and obtain Ambrosetti-Prodi-type results.https://doi.org/10.1515/math-2022-0470periodic solutionsambrosetti-prodi-type resultslower and upper solutionstopological degree39a1239a23 |
| spellingShingle | Zhao Jiao Ma Ruyun Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign Open Mathematics periodic solutions ambrosetti-prodi-type results lower and upper solutions topological degree 39a12 39a23 |
| title | Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign |
| title_full | Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign |
| title_fullStr | Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign |
| title_full_unstemmed | Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign |
| title_short | Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign |
| title_sort | ambrosetti prodi type results for a class of difference equations with nonlinearities indefinite in sign |
| topic | periodic solutions ambrosetti-prodi-type results lower and upper solutions topological degree 39a12 39a23 |
| url | https://doi.org/10.1515/math-2022-0470 |
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