Existence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearity
| dc.contributor.author | Qian, Xiaotao | |
| dc.contributor.author | Chen, Jianqing | |
| dc.date.accessioned | 2022-02-16T20:08:18Z | |
| dc.date.available | 2022-02-16T20:08:18Z | |
| dc.date.issued | 2018-07-17 | |
| dc.description.abstract | In this article, we study the Kirchhoff type problem -(α + ε ∫ℝ3 K(x)|∇u|2dx) div(K(x)∇u) = λK(x)ƒ(x)|u|q-2u + K(x)|u|4u, where x ∈ ℝ3, 1 < q < 2, K(x) = exp(|x|α/4) with α ≥ 2, ε > 0 is small enough, and the parameters α, λ > 0. Under some assumptions on ƒ(x), we establish the existence of two nonnegative nontrivial solutions and obtain uniform lower estimates for extremal values of the problem via variational methods. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 19 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Qian, X., & Chen, J. (2018). Existence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearity. <i>Electronic Journal of Differential Equations, 2018</i>(144), pp. 1-19. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15344 | |
| dc.language.iso | en | |
| dc.publisher | 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, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Variational methods | |
| dc.subject | Kirchhoff type equation | |
| dc.subject | Critical nonlinearity | |
| dc.subject | Multiple solutions | |
| dc.subject | Extremal values | |
| dc.title | Existence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearity | |
| dc.type | Article |