On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential
In this paper, we consider the following Kirchhoff problem −a+b∫R3∇u2dxΔu+λVxu=up−2u, in R3u∈H1R3 where a,b>0 are constants, λ is a positive parameter, and 4<p<6. Under suitable assumptions on Vx, the existence of nontrivial solution is obtained via variational methods. The potential Vx is...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/1735888 |
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| _version_ | 1832558362389118976 |
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| author | Guocui Yang Jianwen Zhou Shengzhong Duan |
| author_facet | Guocui Yang Jianwen Zhou Shengzhong Duan |
| author_sort | Guocui Yang |
| collection | DOAJ |
| description | In this paper, we consider the following Kirchhoff problem −a+b∫R3∇u2dxΔu+λVxu=up−2u, in R3u∈H1R3 where a,b>0 are constants, λ is a positive parameter, and 4<p<6. Under suitable assumptions on Vx, the existence of nontrivial solution is obtained via variational methods. The potential Vx is allowed to be sign-changing. |
| format | Article |
| id | doaj-art-08f77f6ab6cc4cc495688f8b46a0e627 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-08f77f6ab6cc4cc495688f8b46a0e6272025-02-03T01:32:29ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/1735888On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing PotentialGuocui Yang0Jianwen Zhou1Shengzhong Duan2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this paper, we consider the following Kirchhoff problem −a+b∫R3∇u2dxΔu+λVxu=up−2u, in R3u∈H1R3 where a,b>0 are constants, λ is a positive parameter, and 4<p<6. Under suitable assumptions on Vx, the existence of nontrivial solution is obtained via variational methods. The potential Vx is allowed to be sign-changing.http://dx.doi.org/10.1155/2022/1735888 |
| spellingShingle | Guocui Yang Jianwen Zhou Shengzhong Duan On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential Discrete Dynamics in Nature and Society |
| title | On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential |
| title_full | On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential |
| title_fullStr | On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential |
| title_full_unstemmed | On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential |
| title_short | On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential |
| title_sort | on the existence of solutions for a class of schrodinger kirchhoff type equations with sign changing potential |
| url | http://dx.doi.org/10.1155/2022/1735888 |
| work_keys_str_mv | AT guocuiyang ontheexistenceofsolutionsforaclassofschrodingerkirchhofftypeequationswithsignchangingpotential AT jianwenzhou ontheexistenceofsolutionsforaclassofschrodingerkirchhofftypeequationswithsignchangingpotential AT shengzhongduan ontheexistenceofsolutionsforaclassofschrodingerkirchhofftypeequationswithsignchangingpotential |