Multiple Solutions of a p-th Yamabe Equation on Graph
Let G=V,E be a connected finite graph and Δp be the p-Laplacian on G with p>1. We consider a perturbed p-th Yamabe equation −Δpu−λup−2u=huα−2u+εf, where h,f:V⟶ℝ are functions with h,f>0; 1<p<α;λ and ε are two positive constants. Using the variational method, we prove that there exists so...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/5573605 |
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| _version_ | 1832551157586722816 |
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| author | Zhongqi Peng Aimin Zhu Tingting Zhang |
| author_facet | Zhongqi Peng Aimin Zhu Tingting Zhang |
| author_sort | Zhongqi Peng |
| collection | DOAJ |
| description | Let G=V,E be a connected finite graph and Δp be the p-Laplacian on G with p>1. We consider a perturbed p-th Yamabe equation −Δpu−λup−2u=huα−2u+εf, where h,f:V⟶ℝ are functions with h,f>0; 1<p<α;λ and ε are two positive constants. Using the variational method, we prove that there exists some positive constant ϵ1 such that for all ϵ∈0,ϵ1, the above equation has two distinct solutions. |
| format | Article |
| id | doaj-art-fc19a8ff1e04496ebd7b0c7bcd49f198 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-fc19a8ff1e04496ebd7b0c7bcd49f1982025-02-03T06:04:50ZengWileyJournal of Function Spaces2314-88882023-01-01202310.1155/2023/5573605Multiple Solutions of a p-th Yamabe Equation on GraphZhongqi Peng0Aimin Zhu1Tingting Zhang2School of ManagementSchool of ManagementSchool of ManagementLet G=V,E be a connected finite graph and Δp be the p-Laplacian on G with p>1. We consider a perturbed p-th Yamabe equation −Δpu−λup−2u=huα−2u+εf, where h,f:V⟶ℝ are functions with h,f>0; 1<p<α;λ and ε are two positive constants. Using the variational method, we prove that there exists some positive constant ϵ1 such that for all ϵ∈0,ϵ1, the above equation has two distinct solutions.http://dx.doi.org/10.1155/2023/5573605 |
| spellingShingle | Zhongqi Peng Aimin Zhu Tingting Zhang Multiple Solutions of a p-th Yamabe Equation on Graph Journal of Function Spaces |
| title | Multiple Solutions of a p-th Yamabe Equation on Graph |
| title_full | Multiple Solutions of a p-th Yamabe Equation on Graph |
| title_fullStr | Multiple Solutions of a p-th Yamabe Equation on Graph |
| title_full_unstemmed | Multiple Solutions of a p-th Yamabe Equation on Graph |
| title_short | Multiple Solutions of a p-th Yamabe Equation on Graph |
| title_sort | multiple solutions of a p th yamabe equation on graph |
| url | http://dx.doi.org/10.1155/2023/5573605 |
| work_keys_str_mv | AT zhongqipeng multiplesolutionsofapthyamabeequationongraph AT aiminzhu multiplesolutionsofapthyamabeequationongraph AT tingtingzhang multiplesolutionsofapthyamabeequationongraph |