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Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential
Papageorgiou, Nikolaos (Avtor), Rǎdulescu, Vicenţiu (Avtor), Repovš, Dušan (Avtor)

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Izvleček
We study perturbations of the eigenvalue problem for the negative Laplacian plus an indefinite and unbounded potential and Robin boundary condition. First we consider the case of a sublinear perturbation and then of a superlinear perturbation. For the first case we show that for ▫$\lambda < \widehat{\lambda}_{1}$▫ (▫$\widehat{\lambda}_{1}$▫ being the principal eigenvalue) there is one positive solution which is unique under additional conditions on the perturbation term. For ▫$\lambda \geq \widehat{\lambda}_{1}$▫ there are no positive solutions. In the superlinear case, for ▫$\lambda < \widehat{\lambda}_{1}$▫ we have at least two positive solutions and for ▫$\lambda \geq \widehat{\lambda}_{1}$▫ there are no positive solutions. For both cases we establish the existence of a minimal positive solution ▫$\bar{u}_{\lambda}$▫ and we investigate the properties of the map ▫$\lambda \mapsto \bar{u}_{\lambda}$▫.

Jezik:Angleški jezik
Ključne besede:indefinite and unbounded potential, Robin eigenvalue problem, sublinear perturbation, superlinear perturbation, maximum principle, positive solution, minimal positive solution
Vrsta gradiva:Članek v reviji (dk_c)
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:PEF - Pedagoška fakulteta
Leto izida:2017
Št. strani:Str. 2589-2618
Številčenje:Vol. 37, no. 5
UDK:517.956
ISSN pri članku:1078-0947
DOI: http://dx.doi.org/10.3934/dcds.2017111 Povezava se odpre v novem oknu
COBISS.SI-ID:17925721 Povezava se odpre v novem oknu
Število ogledov:309
Število prenosov:245
Metapodatki:XML RDF-CHPDL DC-XML DC-RDF
 
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Naslov:Discrete and continuous dynamical systems
Skrajšan naslov:Discrete contin. dyn. syst.
Založnik:American Institute of Mathematical Sciences
ISSN:1078-0947
COBISS.SI-ID:15865689 Povezava se odpre v novem oknu

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