On Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations
| dc.contributor.author | Binding, Paul A. | |
| dc.contributor.author | Drabek, Pavel | |
| dc.contributor.author | Huang, Yin Xi | |
| dc.date.accessioned | 2018-08-30T14:23:13Z | |
| dc.date.available | 2018-08-30T14:23:13Z | |
| dc.date.issued | 1997-01-30 | |
| dc.description.abstract | We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem {−div (|∇u|p−2</sup> ∇u) = λα(x) |u|p−2 u + b(x)|u|γ−2 u, x ∈ Ω, ∂u / ∂n = 0, x ∈ ∂Ω , where Ω is a smooth bounded domain in ℝ<sup>n</sup>, b changes sign, 1 < p < N, 1 < γ < Np/ (N − p) and γ ≠ p. We prove that (i) if ∫<sub>Ω</sub> α(x) dx ≠ 0 and b satisfies another integral condition, then there exists some λ* such that λ* ∫Ω α(x) dx < 0 and, for λ strictly between 0 and λ*, the problem has a positive solution and (ii) if ∫Ω α(x) dx = 0, then the problem has a positive solution for small λ provided that ∫Ω b(x) dx < 0. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 11 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Binding, P. A., Drabek, P., & Huang, Y. X. (1997). On Neumann boundary value problems for some quasilinear elliptic equations. <i>Electronic Journal of Differential Equations, 1997</i>(05), pp. 1-11. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/7658 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 1997, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | p-Laplacian | |
| dc.subject | positive solutions | |
| dc.subject | Neumann boundary value problems | |
| dc.title | On Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations | |
| dc.type | Article |