Traveling wave solutions for an integrodifference equation of higher order
This article is concerned with the minimal wave speed of traveling wave solutions for an integrodifference equation of higher order. Besides the operator may be nonmonotone, the kernel functions may be not Lebesgue measurable and integrable such that the equation has lower regularity. By constructin...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022902?viewType=HTML |
| _version_ | 1811295160947965952 |
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| author | Fuzhen Wu |
| author_facet | Fuzhen Wu |
| author_sort | Fuzhen Wu |
| collection | DOAJ |
| description | This article is concerned with the minimal wave speed of traveling wave solutions for an integrodifference equation of higher order. Besides the operator may be nonmonotone, the kernel functions may be not Lebesgue measurable and integrable such that the equation has lower regularity. By constructing a proper set of potential wave profiles, we obtain the existence of smooth traveling wave solutions when the wave speed is larger than a threshold. Here, the profile set is obtained by giving a pair of upper and lower solutions. When the wave speed is the threshold, the existence of nontrivial traveling wave solutions is proved by passing to a limit function. Moreover, we obtain the nonexistence of nontrivial traveling wave solutions when the wave speed is smaller than the threshold. |
| first_indexed | 2024-04-13T05:28:44Z |
| format | Article |
| id | doaj.art-3ec41cff67a54838afa28b87d457cbc6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T05:28:44Z |
| publishDate | 2022-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3ec41cff67a54838afa28b87d457cbc62022-12-22T03:00:31ZengAIMS PressAIMS Mathematics2473-69882022-07-0179164821649710.3934/math.2022902Traveling wave solutions for an integrodifference equation of higher orderFuzhen Wu0Digital Information Technology School, Zhejiang Technical Institute of Economics, Hangzhou, Zhejiang 310018, ChinaThis article is concerned with the minimal wave speed of traveling wave solutions for an integrodifference equation of higher order. Besides the operator may be nonmonotone, the kernel functions may be not Lebesgue measurable and integrable such that the equation has lower regularity. By constructing a proper set of potential wave profiles, we obtain the existence of smooth traveling wave solutions when the wave speed is larger than a threshold. Here, the profile set is obtained by giving a pair of upper and lower solutions. When the wave speed is the threshold, the existence of nontrivial traveling wave solutions is proved by passing to a limit function. Moreover, we obtain the nonexistence of nontrivial traveling wave solutions when the wave speed is smaller than the threshold.https://www.aimspress.com/article/doi/10.3934/math.2022902?viewType=HTMLnonmonotone equationupper-lower solutionsfixed point theoremweaker regularityminimal wave speed |
| spellingShingle | Fuzhen Wu Traveling wave solutions for an integrodifference equation of higher order AIMS Mathematics nonmonotone equation upper-lower solutions fixed point theorem weaker regularity minimal wave speed |
| title | Traveling wave solutions for an integrodifference equation of higher order |
| title_full | Traveling wave solutions for an integrodifference equation of higher order |
| title_fullStr | Traveling wave solutions for an integrodifference equation of higher order |
| title_full_unstemmed | Traveling wave solutions for an integrodifference equation of higher order |
| title_short | Traveling wave solutions for an integrodifference equation of higher order |
| title_sort | traveling wave solutions for an integrodifference equation of higher order |
| topic | nonmonotone equation upper-lower solutions fixed point theorem weaker regularity minimal wave speed |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022902?viewType=HTML |
| work_keys_str_mv | AT fuzhenwu travelingwavesolutionsforanintegrodifferenceequationofhigherorder |