Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity
In this paper, we study the following nonlocal problem −a−b∫Ω ∇u2dxΔu=λu+fxup−2u,x∈Ω,u=0,x∈∂Ω, where a,b>0 are constants, 1<p<2, λ>0, f∈L∞Ω is a positive function, and Ω is a smooth bounded domain in ℝN with N≥3. By variational methods, we obtain a pair of nontrivial solutions for the co...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6671882 |
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| author | Zhigao Shi Xiaotao Qian |
| author_facet | Zhigao Shi Xiaotao Qian |
| author_sort | Zhigao Shi |
| collection | DOAJ |
| description | In this paper, we study the following nonlocal problem −a−b∫Ω ∇u2dxΔu=λu+fxup−2u,x∈Ω,u=0,x∈∂Ω, where a,b>0 are constants, 1<p<2, λ>0, f∈L∞Ω is a positive function, and Ω is a smooth bounded domain in ℝN with N≥3. By variational methods, we obtain a pair of nontrivial solutions for the considered problem provided f∞ is small enough. |
| format | Article |
| id | doaj-art-90deffbb7500445ca5345ade7aff64f2 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-90deffbb7500445ca5345ade7aff64f22025-02-03T05:43:48ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/66718826671882Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear NonlinearityZhigao Shi0Xiaotao Qian1Teaching and Research Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, ChinaDepartment of Basic Teaching and Research, Yango University, Fuzhou 350015, ChinaIn this paper, we study the following nonlocal problem −a−b∫Ω ∇u2dxΔu=λu+fxup−2u,x∈Ω,u=0,x∈∂Ω, where a,b>0 are constants, 1<p<2, λ>0, f∈L∞Ω is a positive function, and Ω is a smooth bounded domain in ℝN with N≥3. By variational methods, we obtain a pair of nontrivial solutions for the considered problem provided f∞ is small enough.http://dx.doi.org/10.1155/2021/6671882 |
| spellingShingle | Zhigao Shi Xiaotao Qian Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity Advances in Mathematical Physics |
| title | Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity |
| title_full | Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity |
| title_fullStr | Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity |
| title_full_unstemmed | Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity |
| title_short | Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity |
| title_sort | multiple nontrivial solutions for a nonlocal problem with sublinear nonlinearity |
| url | http://dx.doi.org/10.1155/2021/6671882 |
| work_keys_str_mv | AT zhigaoshi multiplenontrivialsolutionsforanonlocalproblemwithsublinearnonlinearity AT xiaotaoqian multiplenontrivialsolutionsforanonlocalproblemwithsublinearnonlinearity |