Global bifurcation results for a semilinear biharmonic equation on all of IRN

Stavrakakis, NM; Zographopoulos, N

dc.contributor.author	Stavrakakis, NM	en
dc.contributor.author	Zographopoulos, N	en
dc.date.accessioned	2014-03-01T01:48:36Z
dc.date.available	2014-03-01T01:48:36Z
dc.date.issued	1999	en
dc.identifier.issn	02322064	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/25527
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-22844457274&partnerID=40&md5=192be858817beba9aa48ed22570dd14b	en
dc.subject	Biharmonic equations	en
dc.subject	Indefinite weights	en
dc.subject	Local and global bifurcation theory	en
dc.subject	Maximum principle	en
dc.subject	Nonlinear eigenvalue problems	en
dc.title	Global bifurcation results for a semilinear biharmonic equation on all of IRN	en
heal.type	journalArticle	en
heal.publicationDate	1999	en
heal.abstract	We prove existence of positive solutions for the semilinear problem (-Δ)2u = λg(x)f(u), u(x) > 0 (x ∈ ℝN), lim\|x\|→+∞u(x) = 0 under the main hypothesis N > 4 and g ∈ LN/4(ℝN). First, we employ classical spectral analysis for the existence of a simple positive principal eigenvalue for the linearized problem. Next, we prove the existence of a global continuum of positive solutions for the problem above, branching out from the first eigenvalue of the differential equation in the case that f(u) = u. This fact is achieved by applying standard local and global bifurcation theory. It was possible to carry out these methods by working between certain equivalent weighted and homogeneous Sobolev spaces. © Heldermann Verlag.	en
heal.journalName	Zeitschrift fur Analysis und ihre Anwendung	en
dc.identifier.volume	18	en
dc.identifier.issue	3	en
dc.identifier.spage	753	en
dc.identifier.epage	766	en