Existence of two positive solutions for indefinite Kirchhoff equations in R^3
| dc.contributor.author | Ding, Ling | |
| dc.contributor.author | Meng, Yi-Jie | |
| dc.contributor.author | Xiao, Shi-Wu | |
| dc.contributor.author | Zhang, Jin-Ling | |
| dc.date.accessioned | 2023-06-06T20:00:01Z | |
| dc.date.available | 2023-06-06T20:00:01Z | |
| dc.date.issued | 2016-01-25 | |
| dc.description.abstract | In this article we study the Kirchhoff type equation -(1 + b ∫ℝ3 |∇u|2dx) ∆u + u = k(x) ƒ(u) + λh(x)u, x ∈ ℝ3, u ∈ H1(ℝ3), involving a linear part -∆u + u - λh(x)u which is coercive if 0 < λ < λ1(h) and is noncoercive if λ > λ1(h), a nonlocal nonlinear term -b ∫ℝ3 |∇u|2dx∆u and a sign-changing nonlinearity of the form k(x) ƒ(s), where b > 0, λ > 0 is a real parameter and λ1(h) is the first eigenvalue of -∆u + u = λh(x)u. Under suitable assumptions on ƒ and h, we obtain positives solution for λ ∈ (0, λ1(h)) and two positive solutions with a condition on k. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Ding, L., Meng, Y. J., Xiao, S. W., & Zhang, J. L. (2016). Existence of two positive solutions for indefinite Kirchhoff equations in R^3. Electronic Journal of Differential Equations, 2016(35), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16909 | |
| 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, 2016, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Indefinite Kirchhoff equation | |
| dc.subject | Concentration compactness lemma | |
| dc.subject | (PS) condition | |
| dc.subject | Ekeland's variational principle | |
| dc.title | Existence of two positive solutions for indefinite Kirchhoff equations in R^3 | |
| dc.type | Article |