A note on the existence and multiplicity of solutions for sublinear fractional problems
Abstract In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following L K p u = λ f ( x , u ) in Ω , u = 0 in R N ∖ Ω , $$ \begin{aligned} &\mathcal{L}^{p}_{K}u=\lambda f(x,u)&&\text{in }\Om...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-017-0903-9 |
| _version_ | 1819071183580037120 |
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| author | Yongqiang Fu |
| author_facet | Yongqiang Fu |
| author_sort | Yongqiang Fu |
| collection | DOAJ |
| description | Abstract In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following L K p u = λ f ( x , u ) in Ω , u = 0 in R N ∖ Ω , $$ \begin{aligned} &\mathcal{L}^{p}_{K}u=\lambda f(x,u)&&\text{in }\Omega, \\ &u=0&&\text{in }\mathbb{R}^{N}\setminus\Omega, \end{aligned} $$ where L K p $\mathcal{L}^{p}_{K} $ is a nonlocal operator with singular kernel, Ω is an open bounded smooth domain of R N $\mathbb{R}^{N}$ . Our purpose is to generalize the known results for fractional Laplacian equations to fractional p-Laplacian equations. |
| first_indexed | 2024-12-21T17:17:47Z |
| format | Article |
| id | doaj.art-f4d0056bc2874fd9a8a843b7547f7f19 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-21T17:17:47Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-f4d0056bc2874fd9a8a843b7547f7f192022-12-21T18:56:15ZengSpringerOpenBoundary Value Problems1687-27702017-11-012017111510.1186/s13661-017-0903-9A note on the existence and multiplicity of solutions for sublinear fractional problemsYongqiang Fu0Department of Mathematics, Harbin Institute of TechnologyAbstract In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following L K p u = λ f ( x , u ) in Ω , u = 0 in R N ∖ Ω , $$ \begin{aligned} &\mathcal{L}^{p}_{K}u=\lambda f(x,u)&&\text{in }\Omega, \\ &u=0&&\text{in }\mathbb{R}^{N}\setminus\Omega, \end{aligned} $$ where L K p $\mathcal{L}^{p}_{K} $ is a nonlocal operator with singular kernel, Ω is an open bounded smooth domain of R N $\mathbb{R}^{N}$ . Our purpose is to generalize the known results for fractional Laplacian equations to fractional p-Laplacian equations.http://link.springer.com/article/10.1186/s13661-017-0903-9fractional p-Laplacian problemvariational methodmultiple solutions |
| spellingShingle | Yongqiang Fu A note on the existence and multiplicity of solutions for sublinear fractional problems Boundary Value Problems fractional p-Laplacian problem variational method multiple solutions |
| title | A note on the existence and multiplicity of solutions for sublinear fractional problems |
| title_full | A note on the existence and multiplicity of solutions for sublinear fractional problems |
| title_fullStr | A note on the existence and multiplicity of solutions for sublinear fractional problems |
| title_full_unstemmed | A note on the existence and multiplicity of solutions for sublinear fractional problems |
| title_short | A note on the existence and multiplicity of solutions for sublinear fractional problems |
| title_sort | note on the existence and multiplicity of solutions for sublinear fractional problems |
| topic | fractional p-Laplacian problem variational method multiple solutions |
| url | http://link.springer.com/article/10.1186/s13661-017-0903-9 |
| work_keys_str_mv | AT yongqiangfu anoteontheexistenceandmultiplicityofsolutionsforsublinearfractionalproblems AT yongqiangfu noteontheexistenceandmultiplicityofsolutionsforsublinearfractionalproblems |