Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system

In this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV). First, we find some conditions to guarantee the existence and nonexistence of positive solution of the system. Second, we st...

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Autores principales:	Geng Qiuping, Wang Jun, Yang Jing
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	positive solutions bifurcation theory critical points nonlinear schrödinger-korteweg-de vries system 35j61 35j20 35q55 49j40 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/c62e05eada434179b49816ff77005d4a
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spelling	oai:doaj.org-article:c62e05eada434179b49816ff77005d4a2021-12-05T14:10:40ZExistence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system2191-94962191-950X10.1515/anona-2021-0214https://doaj.org/article/c62e05eada434179b49816ff77005d4a2021-11-01T00:00:00Zhttps://doi.org/10.1515/anona-2021-0214https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XIn this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV). First, we find some conditions to guarantee the existence and nonexistence of positive solution of the system. Second, we study the asymptotic behavior of the positive ground state solution. Finally, we use the classical Crandall-Rabinowitz local bifurcation theory to get the nontrivial positive solution. To get these results we encounter some new challenges. By combining the Nehari manifolds constraint method and the delicate energy estimates, we overcome the difficulties and find the two bifurcation branches from one semitrivial solution. This is an new interesting phenomenon but which have not previously been found.Geng QiupingWang JunYang JingDe Gruyterarticlepositive solutionsbifurcation theorycritical pointsnonlinear schrödinger-korteweg-de vries system35j6135j2035q5549j40AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 636-654 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	positive solutions bifurcation theory critical points nonlinear schrödinger-korteweg-de vries system 35j61 35j20 35q55 49j40 Analysis QA299.6-433
spellingShingle	positive solutions bifurcation theory critical points nonlinear schrödinger-korteweg-de vries system 35j61 35j20 35q55 49j40 Analysis QA299.6-433 Geng Qiuping Wang Jun Yang Jing Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system
description	In this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV). First, we find some conditions to guarantee the existence and nonexistence of positive solution of the system. Second, we study the asymptotic behavior of the positive ground state solution. Finally, we use the classical Crandall-Rabinowitz local bifurcation theory to get the nontrivial positive solution. To get these results we encounter some new challenges. By combining the Nehari manifolds constraint method and the delicate energy estimates, we overcome the difficulties and find the two bifurcation branches from one semitrivial solution. This is an new interesting phenomenon but which have not previously been found.
format	article
author	Geng Qiuping Wang Jun Yang Jing
author_facet	Geng Qiuping Wang Jun Yang Jing
author_sort	Geng Qiuping
title	Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system
title_short	Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system
title_full	Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system
title_fullStr	Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system
title_full_unstemmed	Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system
title_sort	existence of multiple nontrivial solutions of the nonlinear schrödinger-korteweg-de vries type system
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/c62e05eada434179b49816ff77005d4a
work_keys_str_mv	AT gengqiuping existenceofmultiplenontrivialsolutionsofthenonlinearschrodingerkortewegdevriestypesystem AT wangjun existenceofmultiplenontrivialsolutionsofthenonlinearschrodingerkortewegdevriestypesystem AT yangjing existenceofmultiplenontrivialsolutionsofthenonlinearschrodingerkortewegdevriestypesystem
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Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system

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