Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: The superdiffusive case

Filippakis, ME; Regan, DO; Papageorgiou, NS

dc.contributor.author	Filippakis, ME	en
dc.contributor.author	Regan, DO	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:34:19Z
dc.date.available	2014-03-01T01:34:19Z
dc.date.issued	2010	en
dc.identifier.issn	1534-0392	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20692
dc.subject	Comparison principle	en
dc.subject	Linking sets	en
dc.subject	Mountain pass theorem	en
dc.subject	P-Laplacian	en
dc.subject	Superdiffusive reaction	en
dc.subject	Truncation techniques	en
dc.subject	Upper-lower solutions	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	P-LAPLACE OPERATOR	en
dc.subject.other	MULTIPLE SOLUTIONS	en
dc.subject.other	EIGENVALUE PROBLEMS	en
dc.subject.other	EXISTENCE	en
dc.subject.other	NONRESONANCE	en
dc.subject.other	DIFFUSION	en
dc.subject.other	RESONANCE	en
dc.subject.other	THEOREMS	en
dc.subject.other	SOBOLEV	en
dc.subject.other	SIGN	en
dc.title	Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: The superdiffusive case	en
heal.type	journalArticle	en
heal.identifier.primary	10.3934/cpaa.2010.9.1507	en
heal.identifier.secondary	http://dx.doi.org/10.3934/cpaa.2010.9.1507	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	We consider a nonlinear elliptic equation of logistic type, driven by the p-Laplacian differential operator with a general superdiffusive reaction. We show that the equation exhibits a bifurcation phenomenon. Namely there is a critical value lambda() of the parameter lambda > 0, such that, if lambda > lambda(), the equation has two nontrivial positive smooth solutions, if lambda = lambda(), then there is one positive solution and finally if lambda is an element of (0, lambda()) then there is no positive solution.	en
heal.publisher	AMER INST MATHEMATICAL SCIENCES	en
heal.journalName	Communications on Pure and Applied Analysis	en
dc.identifier.doi	10.3934/cpaa.2010.9.1507	en
dc.identifier.isi	ISI:000281805200003	en
dc.identifier.volume	9	en
dc.identifier.issue	6	en
dc.identifier.spage	1507	en
dc.identifier.epage	1527	en