Combined effects of singular attractive and asymptotically linear terms in a Kirchhoff Dirichlet problem
In this paper, we consider the following Kirchhoff Dirichlet problem with singular attractive term a + b Z |∇u| 2 dx� ∆u = u −γ + λ f(u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN (N ≥ 3), the parameters a, b, λ, γ > 0 and f(u) is asymptotically linear reaction. In particular, we...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Kirchhoff-Dirichlet-probléma |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.39 |
| Online Access: | http://acta.bibl.u-szeged.hu/88919 |
| Tartalmi kivonat: | In this paper, we consider the following Kirchhoff Dirichlet problem with singular attractive term a + b Z |∇u| 2 dx� ∆u = u −γ + λ f(u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN (N ≥ 3), the parameters a, b, λ, γ > 0 and f(u) is asymptotically linear reaction. In particular, we investigate both the strong singular case (γ ≥ 1) and the weak singular case (0 < γ < 1) employing different techniques to reflect the distinct nature of each scenario. In the first case, ground state solutions are obtained via a direct minimizing methods, while in the latter case we combine variational theory with perturbation methods to prove the existence of ground state solutions for above Kirchhoff problem. |
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| Terjedelem/Fizikai jellemzők: | 14 |
| ISSN: | 1417-3875 |