Multiplicity and concentration of nontrivial solutions for generalized extensible beam equations in R^N
| dc.contributor.author | Sun, Juntao | |
| dc.contributor.author | Wu, Tsung-fang | |
| dc.date.accessioned | 2021-11-05T13:38:54Z | |
| dc.date.available | 2021-11-05T13:38:54Z | |
| dc.date.issued | 2019-03-19 | |
| dc.description.abstract | In this article, we study a class of generalized extensible beam equations with a superlinear nonlinearity Δ2u - M(∥∇u∥2L2) Δu + λV(x)u = ƒ(x, u) in ℝN, u ∈ H2 (ℝN), where N ≥ 3, M(t) = αtδ + b with α, δ > 0 and b ∈ ℝ, λ > 0 is a parameter, V ∈ C(ℝN, ℝ) and ƒ ∈ C(ℝN x ℝ, ℝ). Unlike most other papers on this problem, we allow the constant b to be non-positive, which has the physical significance. Under some suitable assumptions on V(x) and ƒ(x, u), when α is small and λ is large enough, we prove the existence of two nontrivial solutions u(1)α,λ and u(2)α,λ, one of which will blow up as the nonlocal term vanishes. Moreover, u(1)α,λ → u(1)∞ and u(2)α,λ → u(2)∞ strongly in H2(ℝN) as λ → ∞, where u(1)∞ ≠ u(2)∞ ∈ H20(Ω) are nontrivial solutions of Dirichlet BVPs on the bounded domain Ω. Also, the nonexistence of nontrivial solutions is also obtained for α large enough. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 23 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Sun, J., & Tsung-Fang, W. (2019). Multiplicity and concentration of nontrivial solutions for generalized extensible beam equations in R^N. <i>Electronic Journal of Differential Equations, 2019</i>(41), pp. 1-23. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14774 | |
| 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, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Extensible beam equations | |
| dc.subject | Nontrivial solution | |
| dc.subject | Multiplicity | |
| dc.subject | Concentration of solutions | |
| dc.title | Multiplicity and concentration of nontrivial solutions for generalized extensible beam equations in R^N | |
| dc.type | Article |