Solutions to Kirchhoff equations with critical exponent

In this paper, we study the following problems {Δ2u−M(∫Ω|∇u|2dx)Δu=λf(x,u)+|u|2∗−2uinΩu=Δu=0on∂Ω, where 2∗=2NN−4 is the critical exponent. Under some conditions on M and f, we prove the existence of nontrivial solutions by using variational methods.

Bibliographic Details
Main Authors:	El Miloud Hssini, Mohammed Massar, Najib Tsouli
Format:	Article
Language:	English
Published:	Emerald Publishing 2016-01-01
Series:	Arab Journal of Mathematical Sciences
Subjects:	Fourth-order elliptic equations Nonlocal problem Critical exponent Lions principle
Online Access:	http://www.sciencedirect.com/science/article/pii/S1319516615000122

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spelling	doaj-d4ae43756fbc45a68015093656a09bfa2021-05-02T19:15:34ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662016-01-0122113814910.1016/j.ajmsc.2015.04.001Solutions to Kirchhoff equations with critical exponentEl Miloud Hssini0Mohammed Massar1Najib Tsouli2University Mohamed I, Faculty of Sciences, Department of Mathematics, Oujda, MoroccoUniversity Mohamed I, Faculty of Sciences & Techniques, Al-Hoceima, MoroccoUniversity Mohamed I, Faculty of Sciences, Department of Mathematics, Oujda, MoroccoIn this paper, we study the following problems {Δ2u−M(∫Ω\|∇u\|2dx)Δu=λf(x,u)+\|u\|2∗−2uinΩu=Δu=0on∂Ω, where 2∗=2NN−4 is the critical exponent. Under some conditions on M and f, we prove the existence of nontrivial solutions by using variational methods.http://www.sciencedirect.com/science/article/pii/S1319516615000122Fourth-order elliptic equationsNonlocal problemCritical exponentLions principle
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	El Miloud Hssini Mohammed Massar Najib Tsouli
spellingShingle	El Miloud Hssini Mohammed Massar Najib Tsouli Solutions to Kirchhoff equations with critical exponent Arab Journal of Mathematical Sciences Fourth-order elliptic equations Nonlocal problem Critical exponent Lions principle
author_facet	El Miloud Hssini Mohammed Massar Najib Tsouli
author_sort	El Miloud Hssini
title	Solutions to Kirchhoff equations with critical exponent
title_short	Solutions to Kirchhoff equations with critical exponent
title_full	Solutions to Kirchhoff equations with critical exponent
title_fullStr	Solutions to Kirchhoff equations with critical exponent
title_full_unstemmed	Solutions to Kirchhoff equations with critical exponent
title_sort	solutions to kirchhoff equations with critical exponent
publisher	Emerald Publishing
series	Arab Journal of Mathematical Sciences
issn	1319-5166
publishDate	2016-01-01
description	In this paper, we study the following problems {Δ2u−M(∫Ω\|∇u\|2dx)Δu=λf(x,u)+\|u\|2∗−2uinΩu=Δu=0on∂Ω, where 2∗=2NN−4 is the critical exponent. Under some conditions on M and f, we prove the existence of nontrivial solutions by using variational methods.
topic	Fourth-order elliptic equations Nonlocal problem Critical exponent Lions principle
url	http://www.sciencedirect.com/science/article/pii/S1319516615000122
work_keys_str_mv	AT elmiloudhssini solutionstokirchhoffequationswithcriticalexponent AT mohammedmassar solutionstokirchhoffequationswithcriticalexponent AT najibtsouli solutionstokirchhoffequationswithcriticalexponent
_version_	1724163885679771648

Solutions to Kirchhoff equations with critical exponent

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