Existence and multiplicity of nontrivial solutions to the modified Kirchhoff equation without the growth and Ambrosetti-Rabinowitz conditions
The paper focuses on the modified Kirchhoff equation a + b Z RN |∇u| 2 dx� ∆u − u∆(u 2 ) + V(x)u = λ f(u), x ∈ R N, where a, b > 0, V(x) ∈ C(RN, R) and λ < 1 is a positive parameter. We just assume that the nonlinearity f(t) is continuous and superlinear in a neighborhood of t = 0 and at infin...
Elmentve itt :
| Szerzők: | |
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2021
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Kirchhoff-egyenlet, Differenciálegyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2021.1.83 |
| Online Access: | http://acta.bibl.u-szeged.hu/75804 |
| LEADER | 01561nas a2200241 i 4500 | ||
|---|---|---|---|
| 001 | acta75804 | ||
| 005 | 20220523131506.0 | ||
| 008 | 220523s2021 hu o 0|| eng d | ||
| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2021.1.83 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Wang Zhongxiang | |
| 245 | 1 | 0 | |a Existence and multiplicity of nontrivial solutions to the modified Kirchhoff equation without the growth and Ambrosetti-Rabinowitz conditions |h [elektronikus dokumentum] / |c Wang Zhongxiang |
| 260 | |c 2021 | ||
| 300 | |a 18 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a The paper focuses on the modified Kirchhoff equation a + b Z RN |∇u| 2 dx� ∆u − u∆(u 2 ) + V(x)u = λ f(u), x ∈ R N, where a, b > 0, V(x) ∈ C(RN, R) and λ < 1 is a positive parameter. We just assume that the nonlinearity f(t) is continuous and superlinear in a neighborhood of t = 0 and at infinity. By applying the perturbation method and using the cutoff function, we get existence and multiplicity of nontrivial solutions to the revised equation. Then we use the Moser iteration to obtain existence and multiplicity of nontrivial solutions to the above original Kirchhoff equation. Moreover, the nonlinearity f(t) may be supercritical. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Kirchhoff-egyenlet, Differenciálegyenlet | ||
| 700 | 0 | 1 | |a Jia Gao |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/75804/1/ejqtde_2021_083.pdf |z Dokumentum-elérés |