Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth
We study the following generalized quasilinear Schrödinger equations with critical growth -divg2u∇u+gug′u∇u|2+Vxu=λfx,u+guGu|2⁎-2Gu,x∈RN, where λ>0, N≥3, g(s):R→R+ is a C1 even function, g(0)=1, and g′(s)≥0 for all s≥0, where G(u)≔∫0ug(t)dt. Under some suitable conditions, we prove that the equat...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/3615085 |
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| author | Quanqing Li Kaimin Teng Xian Wu |
| author_facet | Quanqing Li Kaimin Teng Xian Wu |
| author_sort | Quanqing Li |
| collection | DOAJ |
| description | We study the following generalized quasilinear Schrödinger equations with critical growth -divg2u∇u+gug′u∇u|2+Vxu=λfx,u+guGu|2⁎-2Gu,x∈RN, where λ>0, N≥3, g(s):R→R+ is a C1 even function, g(0)=1, and g′(s)≥0 for all s≥0, where G(u)≔∫0ug(t)dt. Under some suitable conditions, we prove that the equation has a nontrivial solution by variational method. |
| format | Article |
| id | doaj-art-686953101f9b494d9ec0426bca190e07 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-686953101f9b494d9ec0426bca190e072025-02-03T06:00:23ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/36150853615085Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical GrowthQuanqing Li0Kaimin Teng1Xian Wu2Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaDepartment of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, ChinaDepartment of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092, ChinaWe study the following generalized quasilinear Schrödinger equations with critical growth -divg2u∇u+gug′u∇u|2+Vxu=λfx,u+guGu|2⁎-2Gu,x∈RN, where λ>0, N≥3, g(s):R→R+ is a C1 even function, g(0)=1, and g′(s)≥0 for all s≥0, where G(u)≔∫0ug(t)dt. Under some suitable conditions, we prove that the equation has a nontrivial solution by variational method.http://dx.doi.org/10.1155/2018/3615085 |
| spellingShingle | Quanqing Li Kaimin Teng Xian Wu Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth Advances in Mathematical Physics |
| title | Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth |
| title_full | Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth |
| title_fullStr | Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth |
| title_full_unstemmed | Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth |
| title_short | Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth |
| title_sort | existence of nontrivial solutions for generalized quasilinear schrodinger equations with critical growth |
| url | http://dx.doi.org/10.1155/2018/3615085 |
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