Multiple Sign-Changing Solutions for Kirchhoff-Type Equations
We study the following Kirchhoff-type equations -a+b∫Ω∇u2dxΔu+Vxu=fx,u, in Ω, u=0, in ∂Ω, where Ω is a bounded smooth domain of RN (N=1,2,3), a>0, b≥0, f∈C(Ω¯×R,R), and V∈C(Ω¯,R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive,...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/985986 |
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| author | Xingping Li Xiumei He |
| author_facet | Xingping Li Xiumei He |
| author_sort | Xingping Li |
| collection | DOAJ |
| description | We study the following Kirchhoff-type equations -a+b∫Ω∇u2dxΔu+Vxu=fx,u, in Ω, u=0, in ∂Ω, where Ω is a bounded smooth domain of RN (N=1,2,3), a>0, b≥0, f∈C(Ω¯×R,R), and V∈C(Ω¯,R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if f is odd with respect to its second variable, this problem has infinitely many sign-changing solutions. |
| format | Article |
| id | doaj-art-5ce73802353a4565b4e8850b1bbcaa99 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5ce73802353a4565b4e8850b1bbcaa992025-02-03T05:46:35ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/985986985986Multiple Sign-Changing Solutions for Kirchhoff-Type EquationsXingping Li0Xiumei He1Department of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, ChinaDepartment of Mathematics, Kunming University, Kunming, Yunnan 650214, ChinaWe study the following Kirchhoff-type equations -a+b∫Ω∇u2dxΔu+Vxu=fx,u, in Ω, u=0, in ∂Ω, where Ω is a bounded smooth domain of RN (N=1,2,3), a>0, b≥0, f∈C(Ω¯×R,R), and V∈C(Ω¯,R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if f is odd with respect to its second variable, this problem has infinitely many sign-changing solutions.http://dx.doi.org/10.1155/2015/985986 |
| spellingShingle | Xingping Li Xiumei He Multiple Sign-Changing Solutions for Kirchhoff-Type Equations Discrete Dynamics in Nature and Society |
| title | Multiple Sign-Changing Solutions for Kirchhoff-Type Equations |
| title_full | Multiple Sign-Changing Solutions for Kirchhoff-Type Equations |
| title_fullStr | Multiple Sign-Changing Solutions for Kirchhoff-Type Equations |
| title_full_unstemmed | Multiple Sign-Changing Solutions for Kirchhoff-Type Equations |
| title_short | Multiple Sign-Changing Solutions for Kirchhoff-Type Equations |
| title_sort | multiple sign changing solutions for kirchhoff type equations |
| url | http://dx.doi.org/10.1155/2015/985986 |
| work_keys_str_mv | AT xingpingli multiplesignchangingsolutionsforkirchhofftypeequations AT xiumeihe multiplesignchangingsolutionsforkirchhofftypeequations |