Multiple solutions to boundary value problems for semilinear elliptic equations
| dc.contributor.author | Luyen, Duong | |
| dc.contributor.author | Tri, Nguyen Minh | |
| dc.date.accessioned | 2021-08-26T19:02:26Z | |
| dc.date.available | 2021-08-26T19:02:26Z | |
| dc.date.issued | 2021-05-28 | |
| dc.description.abstract | In this article, we study the multiplicity of weak solutions to the boundary value problem -Δu = ƒ(x, u) + g(x, u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain with smooth boundary in ℝN (N > 2), ƒ(x, ξ) is odd in ξ and g is a perturbation term. Under some growth conditions on ƒ and g, we show that there are infinitely many solutions. Here we do not require that ƒ be continuous or satisfy the Ambrosetti-Rabinowitz (AR) condition. The conditions assumed here are not implied by the ones in [3, 15]. We use the perturbation method Rabinowitz combined with estimating the asymptotic behavior of eigenvalues for Schrödinger's equation. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 12 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Luyen, D. T., & Tri, N. M. (2021). Multiple solutions to boundary value problems for semilinear elliptic equations. <i>Electronic Journal of Differential Equations, 2021</i>(48), pp. 1-12. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14458 | |
| 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, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Semilinear elliptic equations | |
| dc.subject | Multiple solutions | |
| dc.subject | Critical points | |
| dc.subject | Perturbation methods | |
| dc.subject | Boundary value problem | |
| dc.title | Multiple solutions to boundary value problems for semilinear elliptic equations | |
| dc.type | Article |