Pointwise bounds for positive supersolutions of nonlinear elliptic problems involving the p-Laplacian
| dc.contributor.author | Aghajani, Asadollah | |
| dc.contributor.author | Mosleh Tehrani, Alireza | |
| dc.date.accessioned | 2022-03-28T17:43:57Z | |
| dc.date.available | 2022-03-28T17:43:57Z | |
| dc.date.issued | 2017-02-14 | |
| dc.description.abstract | We derive a priori bounds for positive supersolutions of -∆pu = ρ(x)ƒ(u), where p > 1 and ∆p is the p-Laplace operator, in a smooth bounded domain of ℝN with zero Dirichlet boundary conditions. We apply our results to the nonlinear elliptic eigenvalue problem -∆pu = λƒ(u), with Dirichlet boundary condition, where ƒ is a nondecreasing continuous differentiable function on such that ƒ(0) > 0, ƒ(t)1/(p-1) is superlinear at infinity, and give sharp upper and lower bounds for the extremal parameter λ*p. In particular, we consider the nonlinearities ƒ(u) = eu and ƒ(u) = (1 + u)m (m > p - 1) and give explicit estimates on λ*p. As a by-product of our results, we obtain a lower bound for the principal eigenvalue of the p-Laplacian that improves obtained results in the recent literature for some range of p and N. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Aghajani, A., & Mosleh Tehrani, A. (2017). Pointwise bounds for positive supersolutions of nonlinear elliptic problems involving the p-Laplacian. <i>Electronic Journal of Differential Equations, 2017</i>(46), pp. 1-14. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15570 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, 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, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Nonlinear eigenvalue problem | |
| dc.subject | Estimates of principal eigenvalue | |
| dc.subject | Extremal parameter | |
| dc.title | Pointwise bounds for positive supersolutions of nonlinear elliptic problems involving the p-Laplacian | |
| dc.type | Article |