Existence of solutions for singular quasilinear elliptic problems with dependence of the gradient
In this paper we establish existence of solutions to the following boundary value problem involving a p-gradient term −∆pu + g(u)|∇u| p = λu σ + Ψ(x), u > 0 in Ω, u = 0 on ∂Ω, where ∆p := div(|∇u| p−2∇u) is p-Laplacian operator, Ω ⊂ RN (N ≥ 3) is a bounded domain with smooth boundary, 1 < p &l...
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: | Szinguláris egyenlet, Elliptikus egyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.21 |
| Online Access: | http://acta.bibl.u-szeged.hu/88901 |
| Tartalmi kivonat: | In this paper we establish existence of solutions to the following boundary value problem involving a p-gradient term −∆pu + g(u)|∇u| p = λu σ + Ψ(x), u > 0 in Ω, u = 0 on ∂Ω, where ∆p := div(|∇u| p−2∇u) is p-Laplacian operator, Ω ⊂ RN (N ≥ 3) is a bounded domain with smooth boundary, 1 < p < N, 0 < σ < p ∗ − 1 with p := pN/ (N − p), Ψ is a measurable function and g(s) ≥ 0 is a continuous function on the interval (0, +∞) which may have a singularity at the origin, i.e. g(s) → +∞ as s → 0. Using the topological degree theory, under certain assumptions on Ψ, we prove the existence of a continuum of positive solutions. |
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| Terjedelem/Fizikai jellemzők: | 27 |
| ISSN: | 1417-3875 |