dc.contributor.author Kandilakis, Dimitrios A. ( ) dc.date.accessioned 2021-05-24T18:57:10Z dc.date.available 2021-05-24T18:57:10Z dc.date.issued 2005-05-31 dc.identifier.citation Kandilakis, D. A. (2005). A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions in unbounded domains. Electronic Journal of Differential Equations, 2005(57), pp. 1-12. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/13640 dc.description.abstract We study the following quasilinear problem with nonlinear boundary conditions -∆pu = λα(x)|u|p-2 u + k(x)|u|q-2 u - h(x)|u|s-2 u, in Ω, |∇u|p-2 ∇u ∙ η + b(x)|u|p-2u = 0 on ∂Ω, where Ω is an unbounded domain in ℝN with a noncompact and smooth boundary ∂Ω, η denotes the unit outward normal vector on ∂Ω, ∆pu = div(|∇u|p-2∇u) is the p-Laplacian, α, k, h and b are nonnegative essentially bounded functions, q < p < s and p* < s. The properties of the first eigenvalue λ1 and the associated eigenvectors of the related eigenvalue problem are examined. Then it is shown that if λ < λ1, the original problem admits an infinite number of solutions one of which is nonnegative, which if λ = λ1 it admits at least one nonnegative solution. Our approach is variational in character. dc.format Text dc.format.extent 12 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University-San Marcos, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Variational methods en_US dc.subject Fibering method en_US dc.subject Palais-Smale condition en_US dc.subject Genus en_US dc.title A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions in unbounded domains en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License. dc.description.department Mathematics
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