Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation

In this paper, we study the following generalized Kadomtsev-Petviashvili equation ut+uxxx+(h(u))x=Dx−1Δyu,{u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where (t,x,y)∈R+×R×RN−1\left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R}}\times {{\mathbb{R}}}^{N-1}, N≥2N\ge 2, Dx−1f(x,y...

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Autores principales:	Zhu Yuting, Chen Chunfang, Chen Jianhua, Yuan Chenggui
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	generalized kadomtsev-petviashvili equation ground state solutions multiplicity of solutions 35j60 35j20 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1e67d86965ab46398b40074303025a7c
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spelling	oai:doaj.org-article:1e67d86965ab46398b40074303025a7c2021-12-05T14:10:52ZMultiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation2391-545510.1515/math-2021-0014https://doaj.org/article/1e67d86965ab46398b40074303025a7c2021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0014https://doaj.org/toc/2391-5455In this paper, we study the following generalized Kadomtsev-Petviashvili equation ut+uxxx+(h(u))x=Dx−1Δyu,{u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where (t,x,y)∈R+×R×RN−1\left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R}}\times {{\mathbb{R}}}^{N-1}, N≥2N\ge 2, Dx−1f(x,y)=∫−∞xf(s,y)ds{D}_{x}^{-1}f\left(x,y)={\int }_{-\infty }^{x}f\left(s,y){\rm{d}}s, ft=∂f∂t{f}_{t}=\frac{\partial f}{\partial t}, fx=∂f∂x{f}_{x}=\frac{\partial f}{\partial x} and Δy=∑i=1N−1∂2∂yi2{\Delta }_{y}={\sum }_{i=1}^{N-1}\frac{{\partial }^{2}}{{\partial }_{{y}_{i}}^{2}}. We get the existence of infinitely many nontrivial solutions under certain assumptions in bounded domain without Ambrosetti-Rabinowitz condition. Moreover, by using the method developed by Jeanjean [13], we establish the existence of ground state solutions in RN{{\mathbb{R}}}^{N}.Zhu YutingChen ChunfangChen JianhuaYuan ChengguiDe Gruyterarticlegeneralized kadomtsev-petviashvili equationground state solutionsmultiplicity of solutions35j6035j20MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 297-305 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	generalized kadomtsev-petviashvili equation ground state solutions multiplicity of solutions 35j60 35j20 Mathematics QA1-939
spellingShingle	generalized kadomtsev-petviashvili equation ground state solutions multiplicity of solutions 35j60 35j20 Mathematics QA1-939 Zhu Yuting Chen Chunfang Chen Jianhua Yuan Chenggui Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation
description	In this paper, we study the following generalized Kadomtsev-Petviashvili equation ut+uxxx+(h(u))x=Dx−1Δyu,{u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where (t,x,y)∈R+×R×RN−1\left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R}}\times {{\mathbb{R}}}^{N-1}, N≥2N\ge 2, Dx−1f(x,y)=∫−∞xf(s,y)ds{D}_{x}^{-1}f\left(x,y)={\int }_{-\infty }^{x}f\left(s,y){\rm{d}}s, ft=∂f∂t{f}_{t}=\frac{\partial f}{\partial t}, fx=∂f∂x{f}_{x}=\frac{\partial f}{\partial x} and Δy=∑i=1N−1∂2∂yi2{\Delta }_{y}={\sum }_{i=1}^{N-1}\frac{{\partial }^{2}}{{\partial }_{{y}_{i}}^{2}}. We get the existence of infinitely many nontrivial solutions under certain assumptions in bounded domain without Ambrosetti-Rabinowitz condition. Moreover, by using the method developed by Jeanjean [13], we establish the existence of ground state solutions in RN{{\mathbb{R}}}^{N}.
format	article
author	Zhu Yuting Chen Chunfang Chen Jianhua Yuan Chenggui
author_facet	Zhu Yuting Chen Chunfang Chen Jianhua Yuan Chenggui
author_sort	Zhu Yuting
title	Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation
title_short	Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation
title_full	Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation
title_fullStr	Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation
title_full_unstemmed	Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation
title_sort	multiple solutions and ground state solutions for a class of generalized kadomtsev-petviashvili equation
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/1e67d86965ab46398b40074303025a7c
work_keys_str_mv	AT zhuyuting multiplesolutionsandgroundstatesolutionsforaclassofgeneralizedkadomtsevpetviashviliequation AT chenchunfang multiplesolutionsandgroundstatesolutionsforaclassofgeneralizedkadomtsevpetviashviliequation AT chenjianhua multiplesolutionsandgroundstatesolutionsforaclassofgeneralizedkadomtsevpetviashviliequation AT yuanchenggui multiplesolutionsandgroundstatesolutionsforaclassofgeneralizedkadomtsevpetviashviliequation
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Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation

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