Existence of positive solutions of elliptic equations with Hardy term
This paper is devoted to studying the existence of positive solutions of the problem: −∆u = u p |x| a + h(x, u, ∇u), inΩ, u = 0, on ∂Ω, where Ω ⊂ RN(N ≥ 3) is an open bounded smooth domain with boundary ∂Ω, and 1 < p < N−a N−2 , 0 < a < 2. Under suitable conditions of h(x, u, ∇u), we get...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2024
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Hardy-tagú elliptikus egyenlet, Differenciálegyenlet - parciális, Spektrálelmélet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2024.1.1 |
| Online Access: | http://acta.bibl.u-szeged.hu/88803 |
| Tartalmi kivonat: | This paper is devoted to studying the existence of positive solutions of the problem: −∆u = u p |x| a + h(x, u, ∇u), inΩ, u = 0, on ∂Ω, where Ω ⊂ RN(N ≥ 3) is an open bounded smooth domain with boundary ∂Ω, and 1 < p < N−a N−2 , 0 < a < 2. Under suitable conditions of h(x, u, ∇u), we get a priori estimates for the positive solutions of problem (∗). By making use of these estimates and topological degree theory, we further obtain some existence results for the positive solutions of problem (∗) when 1 < p < N−a N−2. |
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| Terjedelem/Fizikai jellemzők: | 14 |
| ISSN: | 1417-3875 |