Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition
In this paper, we investigate the following Kirchhoff type problem involving the fractional px-Laplacian operator. a−b∫Ω×Ωux−uypx,y/px,yx−yN+spx,ydxdyLu=λuqx−2u+fx,ux∈Ωu=0 x∈∂Ω,, where Ω is a bounded domain in ℝN with Lipschitz boundary, a≥b>0 are constants, px,y is a function defined on Ω¯×Ω¯, s...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/8888078 |
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| author | Weichun Bu Tianqing An Guoju Ye Said Taarabti |
| author_facet | Weichun Bu Tianqing An Guoju Ye Said Taarabti |
| author_sort | Weichun Bu |
| collection | DOAJ |
| description | In this paper, we investigate the following Kirchhoff type problem involving the fractional px-Laplacian operator. a−b∫Ω×Ωux−uypx,y/px,yx−yN+spx,ydxdyLu=λuqx−2u+fx,ux∈Ωu=0 x∈∂Ω,, where Ω is a bounded domain in ℝN with Lipschitz boundary, a≥b>0 are constants, px,y is a function defined on Ω¯×Ω¯, s∈0,1, and qx>1, Lu is the fractional px-Laplacian operator, N>spx,y, for any x,y∈Ω¯×Ω¯, px∗=px,xN/N−spx,x, λ is a given positive parameter, and f is a continuous function. By using Ekeland’s variational principle and dual fountain theorem, we obtain some new existence and multiplicity of negative energy solutions for the above problem without the Ambrosetti-Rabinowitz ((AR) for short) condition. |
| format | Article |
| id | doaj-art-103ab518fabc46469210f511d3069566 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-103ab518fabc46469210f511d30695662025-02-03T01:20:50ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/88880788888078Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) ConditionWeichun Bu0Tianqing An1Guoju Ye2Said Taarabti3College of Science, Hohai University, Nanjing 210098, ChinaCollege of Science, Hohai University, Nanjing 210098, ChinaCollege of Science, Hohai University, Nanjing 210098, ChinaLaboratory of Systems Engineering and Information Technologies, National School of Applied Sciences of Agadir, Ibn Zohr University, MoroccoIn this paper, we investigate the following Kirchhoff type problem involving the fractional px-Laplacian operator. a−b∫Ω×Ωux−uypx,y/px,yx−yN+spx,ydxdyLu=λuqx−2u+fx,ux∈Ωu=0 x∈∂Ω,, where Ω is a bounded domain in ℝN with Lipschitz boundary, a≥b>0 are constants, px,y is a function defined on Ω¯×Ω¯, s∈0,1, and qx>1, Lu is the fractional px-Laplacian operator, N>spx,y, for any x,y∈Ω¯×Ω¯, px∗=px,xN/N−spx,x, λ is a given positive parameter, and f is a continuous function. By using Ekeland’s variational principle and dual fountain theorem, we obtain some new existence and multiplicity of negative energy solutions for the above problem without the Ambrosetti-Rabinowitz ((AR) for short) condition.http://dx.doi.org/10.1155/2021/8888078 |
| spellingShingle | Weichun Bu Tianqing An Guoju Ye Said Taarabti Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition Journal of Function Spaces |
| title | Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition |
| title_full | Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition |
| title_fullStr | Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition |
| title_full_unstemmed | Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition |
| title_short | Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition |
| title_sort | negative energy solutions for a new fractional px kirchhoff problem without the ar condition |
| url | http://dx.doi.org/10.1155/2021/8888078 |
| work_keys_str_mv | AT weichunbu negativeenergysolutionsforanewfractionalpxkirchhoffproblemwithoutthearcondition AT tianqingan negativeenergysolutionsforanewfractionalpxkirchhoffproblemwithoutthearcondition AT guojuye negativeenergysolutionsforanewfractionalpxkirchhoffproblemwithoutthearcondition AT saidtaarabti negativeenergysolutionsforanewfractionalpxkirchhoffproblemwithoutthearcondition |