Global Bifurcation Results for Semilinear Elliptic Equations on R N: The Fredholm Case

Stavrakakis, NM

dc.contributor.author	Stavrakakis, NM	en
dc.date.accessioned	2014-03-01T01:13:47Z
dc.date.available	2014-03-01T01:13:47Z
dc.date.issued	1998	en
dc.identifier.issn	0022-0396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12719
dc.subject	Bifurcation theory	en
dc.subject	Fredholm (noncompact) operators	en
dc.subject	nonlinear elliptic equation	en
dc.subject	unbounded domains	en
dc.subject	indefinite weights	en
dc.subject	weighted sobolev spaces	en
dc.subject	spectral theory	en
dc.subject.classification	Mathematics	en
dc.subject.other	INDEFINITE WEIGHT FUNCTION	en
dc.subject.other	PRINCIPAL EIGENVALUES	en
dc.title	Global Bifurcation Results for Semilinear Elliptic Equations on R N: The Fredholm Case	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jdeq.1997.3346	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jdeq.1997.3346	en
heal.language	English	en
heal.publicationDate	1998	en
heal.abstract	We prove the existence of a continuum of positive solutions for the semilinear elliptic equation -Delta u(x) = lambda g(x) f(u(x)), 0<u<1 for x epsilon R-N, lim(/x/-->+infinity)u(x)=0, which arises in population genetics, under the hypotheses that N greater than or equal to 3 and the weight g changes sign, being negative and away from zero at ca. After establishing the existence of a simple positive principal eigenvalue E., for the corresponding linearized problem, we prove the existence of a continuum of solutions lying in the space R x H-2 extended from lambda(1) to infinity. To complete this task we state a new version of the global bifurcation theory for nonlinear Fredholm (noncompact) operators and prove the compactness of the solution set of the problem. (C) 1998 Academic Press.	en
heal.publisher	ACADEMIC PRESS INC	en
heal.journalName	Journal of Differential Equations	en
dc.identifier.doi	10.1006/jdeq.1997.3346	en
dc.identifier.isi	ISI:000071872900005	en
dc.identifier.volume	142	en
dc.identifier.issue	1	en
dc.identifier.spage	97	en
dc.identifier.epage	122	en