MULTIPLE SOLUTIONS FOR NONLINEAR NEUMANN PROBLEMS DRIVEN BY A NONHOMOGENEOUS DIFFERENTIAL OPERATOR

Motreanu, D; Papageorgiou, NS

dc.contributor.author	Motreanu, D	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T02:05:26Z
dc.date.available	2014-03-01T02:05:26Z
dc.date.issued	2011	en
dc.identifier.issn	0002-9939	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29479
dc.subject	Nonlinear Neumann problem	en
dc.subject	p-Laplacian	en
dc.subject	local minimizers	en
dc.subject	mountain pass theorem	en
dc.subject	second deformation theorem	en
dc.subject	nonlinear regularity theory	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	LINEAR ELLIPTIC-EQUATIONS	en
dc.subject.other	P-LAPLACIAN	en
dc.subject.other	LOCAL MINIMIZERS	en
dc.subject.other	EXISTENCE	en
dc.subject.other	SIGN	en
dc.title	MULTIPLE SOLUTIONS FOR NONLINEAR NEUMANN PROBLEMS DRIVEN BY A NONHOMOGENEOUS DIFFERENTIAL OPERATOR	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	We consider a nonlinear Neumann problem driven by a nonhomogeneous quasilinear degenerate elliptic differential operator div a(x, del u), a special case of which is the p-Laplacian. The reaction term is a Caratheodory function f (x, s) which exhibits subcritical growth in s. Using variational methods based on the mountain pass and second deformation theorems, together with truncation and minimization techniques, we show that the problem has three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). A crucial tool in our analysis is a result of independent interest which we prove here and which relates W-1,W-P and C-1 local minimizers of a C-1-functional constructed with the general differential operator div a(x, del u).	en
heal.publisher	AMER MATHEMATICAL SOC	en
heal.journalName	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY	en
dc.identifier.isi	ISI:000295432600014	en
dc.identifier.volume	139	en
dc.identifier.issue	10	en
dc.identifier.spage	3527	en
dc.identifier.epage	3535	en