Oscillatory property of solutions to nonlinear eigenvalue problems
This paper is concerned with the nonlinear eigenvalue problem −u 00(t) = λ (u(t) + g(u(t))), u(t) > 0, t ∈ I := (−1, 1), u(±1) = 0, where g(u) = u p sin(u q ) (0 ≤ p < 1, 0 < q ≤ 1) and λ > 0 is a bifurcation parameter. It is known that, for a given α > 0, there exists a unique soluti...
Elmentve itt :
| Szerző: | |
|---|---|
| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
|
| Sorozat: | Electronic journal of qualitative theory of differential equations
|
| Kulcsszavak: | Oszcilláció - differenciálegyenlet, Bifurkáció |
| doi: | 10.14232/ejqtde.2019.1.67 |
| Online Access: | http://acta.bibl.u-szeged.hu/62291 |
| LEADER | 01474nas a2200205 i 4500 | ||
|---|---|---|---|
| 001 | acta62291 | ||
| 005 | 20210916104232.0 | ||
| 008 | 190930s2019 hu o 0|| zxx d | ||
| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2019.1.67 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a zxx | ||
| 100 | 1 | |a Shibata Tetsutaro | |
| 245 | 1 | 0 | |a Oscillatory property of solutions to nonlinear eigenvalue problems |h [elektronikus dokumentum] / |c Shibata Tetsutaro |
| 260 | |c 2019 | ||
| 300 | |a 1-9 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a This paper is concerned with the nonlinear eigenvalue problem −u 00(t) = λ (u(t) + g(u(t))), u(t) > 0, t ∈ I := (−1, 1), u(±1) = 0, where g(u) = u p sin(u q ) (0 ≤ p < 1, 0 < q ≤ 1) and λ > 0 is a bifurcation parameter. It is known that, for a given α > 0, there exists a unique solution pair (λ(α), uα) ∈ R+ × C 2 (I) satisfying α = kuαk∞ (= uα(0)). We establish the precise asymptotic formula for L r -norm kuαkr (1 ≤ r < ∞) of the solution uα as α → ∞ to show the evidence that uα(t) is oscillatory as α → ∞. We also obtain the asymptotic formula for λ in L r -framework, which has different property from that for diffusive logistic equation of population dynamics. | |
| 695 | |a Oszcilláció - differenciálegyenlet, Bifurkáció | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/62291/1/ejqtde_2019_067_001-009.pdf |z Dokumentum-elérés |