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Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potentialPapageorgiou, Nikolaos, 1958- ; Rǎdulescu, Vicenţiu, 1958- ; Repovš, Dušan, 1954-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 ▫$\lambda \mapsto \bar{u}_{\lambda}$▫.Source: Discrete and continuous dynamical systems. - ISSN 1078-0947 (Vol. 37, no. 5, 2017, str. 2589-2618)Type of material - article, component partPublish date - 2017Language - englishCOBISS.SI-ID - 17925721
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source: Discrete and continuous dynamical systems. - ISSN 1078-0947 (Vol. 37, no. 5, 2017, str. 2589-2618)
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Papageorgiou, Nikolaos, 1958- | 38771 |
Rǎdulescu, Vicenţiu, 1958- | 29964 |
Repovš, Dušan, 1954- | 07083 |
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