Nonlinear perturbations of the Kirchhoff equation
| dc.contributor.author | Miranda, Manuel M. | |
| dc.contributor.author | Louredo, Aldo T. | |
| dc.contributor.author | Medeiros, Luiz A. | |
| dc.date.accessioned | 2022-04-06T15:25:30Z | |
| dc.date.available | 2022-04-06T15:25:30Z | |
| dc.date.issued | 2017-03-21 | |
| dc.description.abstract | In this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation u″ - M(t, ∥u(t)∥2)∆u + |u|ρ = ƒ in Ω x (0, T0), u = 0 on Γ0 x]0, T0[, ∂u/∂v + δh(u′) = 0 on Γ1 x]0, T0[, where Ω is a bounded domain of ℝn with its boundary consisting of two disjoint parts Γ0 and Γ1; ρ > 1 is a real number; v(x) is the exterior unit normal vector at x ∈ Γ1 and δ(x), h(s) are real functions defined in Γ1 and ℝ, respectively. Our result is obtained using the Galerkin method with a special basis, the Tartar argument, the compactness approach, and a Fixed-Point method. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Miranda, M. M., Louredo, A. T., & Medeiros, L. A. (2017). Nonlinear perturbations of the Kirchhoff equation. <i>Electronic Journal of Differential Equations, 2017</i>(77), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15609 | |
| 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, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Kirchhoff equation | |
| dc.subject | Nonlinear boundary condition | |
| dc.subject | Existence of solutions | |
| dc.title | Nonlinear perturbations of the Kirchhoff equation | |
| dc.type | Article |