The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity
In this paper, we firstly discuss the existence of the least energy sign-changing solutions for a class of p-Kirchhoff-type problems with a (2p-1)-linear growth nonlinearity. The quantitative deformation lemma and Non-Nehari manifold method are used in the paper to prove the main results. Remarkably...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/3713909 |
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| author | Jiangyan Yao Wei Han |
| author_facet | Jiangyan Yao Wei Han |
| author_sort | Jiangyan Yao |
| collection | DOAJ |
| description | In this paper, we firstly discuss the existence of the least energy sign-changing solutions for a class of p-Kirchhoff-type problems with a (2p-1)-linear growth nonlinearity. The quantitative deformation lemma and Non-Nehari manifold method are used in the paper to prove the main results. Remarkably, we use a new method to verify that Mb≠∅. The main results of our paper are the existence of the least energy sign-changing solution and its corresponding energy doubling property. Moreover, we also give the convergence property of the least energy sign-changing solution as the parameter b↘0. |
| format | Article |
| id | doaj-art-d21941288ac94f92a163a8353e182700 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d21941288ac94f92a163a8353e1827002025-02-03T01:32:40ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/37139093713909The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth NonlinearityJiangyan Yao0Wei Han1Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaIn this paper, we firstly discuss the existence of the least energy sign-changing solutions for a class of p-Kirchhoff-type problems with a (2p-1)-linear growth nonlinearity. The quantitative deformation lemma and Non-Nehari manifold method are used in the paper to prove the main results. Remarkably, we use a new method to verify that Mb≠∅. The main results of our paper are the existence of the least energy sign-changing solution and its corresponding energy doubling property. Moreover, we also give the convergence property of the least energy sign-changing solution as the parameter b↘0.http://dx.doi.org/10.1155/2019/3713909 |
| spellingShingle | Jiangyan Yao Wei Han The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity Discrete Dynamics in Nature and Society |
| title | The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity |
| title_full | The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity |
| title_fullStr | The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity |
| title_full_unstemmed | The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity |
| title_short | The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity |
| title_sort | existence result for a class of p kirchhoff type problem with a multilinear growth nonlinearity |
| url | http://dx.doi.org/10.1155/2019/3713909 |
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