Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth
In this paper, we are devoted to establishing that the existence of positive solutions for a class of generalized quasilinear elliptic equations in $\mathbb{R}^{N}$ with Sobolev critical growth, which have appeared from plasma physics, as well as high-power ultrashort laser in matter. To begin, by c...
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University of Szeged
2024-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10658 |
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| author | Nian Zhang Chuchu Liang |
| author_facet | Nian Zhang Chuchu Liang |
| author_sort | Nian Zhang |
| collection | DOAJ |
| description | In this paper, we are devoted to establishing that the existence of positive solutions for a class of generalized quasilinear elliptic equations in $\mathbb{R}^{N}$ with Sobolev critical growth, which have appeared from plasma physics, as well as high-power ultrashort laser in matter. To begin, by changing the variable, quasilinear equations are transformed into semilinear equations. The positive solutions to semilinear equations are then presented using the Mountain Pass Theorem for locally Lipschitz functionals and the Concentration-Compactness Principle. Finally, an inverse translation reveals the presence of positive solutions to the original quasilinear equations. |
| format | Article |
| id | doaj-art-3c696c9eed8b42a69ec5fe2ca84f7b38 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-3c696c9eed8b42a69ec5fe2ca84f7b382025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-08-0120244412510.14232/ejqtde.2024.1.4410658Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growthNian Zhang0Chuchu LiangSchool of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, ChinaIn this paper, we are devoted to establishing that the existence of positive solutions for a class of generalized quasilinear elliptic equations in $\mathbb{R}^{N}$ with Sobolev critical growth, which have appeared from plasma physics, as well as high-power ultrashort laser in matter. To begin, by changing the variable, quasilinear equations are transformed into semilinear equations. The positive solutions to semilinear equations are then presented using the Mountain Pass Theorem for locally Lipschitz functionals and the Concentration-Compactness Principle. Finally, an inverse translation reveals the presence of positive solutions to the original quasilinear equations.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10658variational methodssobolev critical growthlocally lipschitz functional |
| spellingShingle | Nian Zhang Chuchu Liang Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth Electronic Journal of Qualitative Theory of Differential Equations variational methods sobolev critical growth locally lipschitz functional |
| title | Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth |
| title_full | Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth |
| title_fullStr | Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth |
| title_full_unstemmed | Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth |
| title_short | Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth |
| title_sort | existence of positive solutions for generalized quasilinear schrodinger equations with sobolev critical growth |
| topic | variational methods sobolev critical growth locally lipschitz functional |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10658 |
| work_keys_str_mv | AT nianzhang existenceofpositivesolutionsforgeneralizedquasilinearschrodingerequationswithsobolevcriticalgrowth AT chuchuliang existenceofpositivesolutionsforgeneralizedquasilinearschrodingerequationswithsobolevcriticalgrowth |