Positive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems

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dc.contributor.authorPapageorgiou, Nikolaos S.
dc.contributor.authorVetro, Catogero
dc.contributor.authorVetro, Francesca
dc.date.accessioned2021-09-21T14:36:05Z
dc.date.available2021-09-21T14:36:05Z
dc.date.issued2020-01-24
dc.description.abstractWe consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.
dc.description.departmentMathematics
dc.formatText
dc.format.extent20 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationPapageorgiou, N. S., Vetro, C., & Vetro, F. (2020). Positive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems. <i>Electronic Journal of Differential Equations, 2020</i>(12), pp. 1-20.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14516
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectNonlinear nonhomogeneous differential operator
dc.subjectNonlinear Regularity Theory
dc.subjectNonlinear maximum principle
dc.subjectStrong comparison
dc.subjectBifurcation-type theorem
dc.subjectNodal solution
dc.subjectCritical group
dc.titlePositive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems
dc.typeArticle

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