Infinitely many positive solutions for a double phase problem

Abstract This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the existence of infinitely many positive solutions whose W 0 1 , H ( Ω ) $W_{0}^{1,H...

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Main Authors:	Bei-Lei Zhang, Bin Ge, Gang-Ling Hou
Format:	Article
Language:	English
Published:	SpringerOpen 2020-08-01
Series:	Boundary Value Problems
Subjects:	Double phase operator Multiple solutions Variational methods
Online Access:	http://link.springer.com/article/10.1186/s13661-020-01439-9

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spelling	doaj-b3a5762ec466493ca64d0e3537812c1f2020-11-25T03:51:35ZengSpringerOpenBoundary Value Problems1687-27702020-08-012020111010.1186/s13661-020-01439-9Infinitely many positive solutions for a double phase problemBei-Lei Zhang0Bin Ge1Gang-Ling Hou2School of Mathematical Sciences, Harbin Engineering UniversitySchool of Mathematical Sciences, Harbin Engineering UniversityCollege of Aerospace and Civil Engineering, Harbin Engineering UniversityAbstract This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the existence of infinitely many positive solutions whose W 0 1 , H ( Ω ) $W_{0}^{1,H}(\varOmega )$ -norms and L ∞ $L^{\infty }$ -norms tend to zero under suitable hypotheses about nonlinearity.http://link.springer.com/article/10.1186/s13661-020-01439-9Double phase operatorMultiple solutionsVariational methods
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bei-Lei Zhang Bin Ge Gang-Ling Hou
spellingShingle	Bei-Lei Zhang Bin Ge Gang-Ling Hou Infinitely many positive solutions for a double phase problem Boundary Value Problems Double phase operator Multiple solutions Variational methods
author_facet	Bei-Lei Zhang Bin Ge Gang-Ling Hou
author_sort	Bei-Lei Zhang
title	Infinitely many positive solutions for a double phase problem
title_short	Infinitely many positive solutions for a double phase problem
title_full	Infinitely many positive solutions for a double phase problem
title_fullStr	Infinitely many positive solutions for a double phase problem
title_full_unstemmed	Infinitely many positive solutions for a double phase problem
title_sort	infinitely many positive solutions for a double phase problem
publisher	SpringerOpen
series	Boundary Value Problems
issn	1687-2770
publishDate	2020-08-01
description	Abstract This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the existence of infinitely many positive solutions whose W 0 1 , H ( Ω ) $W_{0}^{1,H}(\varOmega )$ -norms and L ∞ $L^{\infty }$ -norms tend to zero under suitable hypotheses about nonlinearity.
topic	Double phase operator Multiple solutions Variational methods
url	http://link.springer.com/article/10.1186/s13661-020-01439-9
work_keys_str_mv	AT beileizhang infinitelymanypositivesolutionsforadoublephaseproblem AT binge infinitelymanypositivesolutionsforadoublephaseproblem AT ganglinghou infinitelymanypositivesolutionsforadoublephaseproblem
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Infinitely many positive solutions for a double phase problem

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