Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN
The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter λ on RN is proved by using variational method. We will show that if the nonlinearities are asymptotically linear at infinity and λ>0 is sufficiently small, the Kirchhoff type equations have at...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2016/9503073 |
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| _version_ | 1832549678281916416 |
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| author | Yu Duan Chun-Lei Tang |
| author_facet | Yu Duan Chun-Lei Tang |
| author_sort | Yu Duan |
| collection | DOAJ |
| description | The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter λ on RN is proved by using variational method. We will show that if the nonlinearities are asymptotically linear at infinity and λ>0 is sufficiently small, the Kirchhoff type equations have at least two positive solutions. For the perturbed problem, we give the result of existence of three positive solutions. |
| format | Article |
| id | doaj-art-b00debf1eee24fddb14963f266c123a3 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-b00debf1eee24fddb14963f266c123a32025-02-03T06:10:50ZengWileyInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/95030739503073Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RNYu Duan0Chun-Lei Tang1School of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaThe multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter λ on RN is proved by using variational method. We will show that if the nonlinearities are asymptotically linear at infinity and λ>0 is sufficiently small, the Kirchhoff type equations have at least two positive solutions. For the perturbed problem, we give the result of existence of three positive solutions.http://dx.doi.org/10.1155/2016/9503073 |
| spellingShingle | Yu Duan Chun-Lei Tang Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN International Journal of Differential Equations |
| title | Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN |
| title_full | Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN |
| title_fullStr | Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN |
| title_full_unstemmed | Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN |
| title_short | Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN |
| title_sort | multiple solutions for the asymptotically linear kirchhoff type equations on rn |
| url | http://dx.doi.org/10.1155/2016/9503073 |
| work_keys_str_mv | AT yuduan multiplesolutionsfortheasymptoticallylinearkirchhofftypeequationsonrn AT chunleitang multiplesolutionsfortheasymptoticallylinearkirchhofftypeequationsonrn |