A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions in unbounded domains
| 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.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.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 12 pages | |
| dc.format.medium | 1 file (.pdf) | |
| 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. <i>Electronic Journal of Differential Equations, 2005</i>(57), pp. 1-12. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13640 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| 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 | |
| dc.subject | Fibering method | |
| dc.subject | Palais-Smale condition | |
| dc.subject | Genus | |
| dc.title | A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions in unbounded domains | |
| dc.type | Article |