A critical elliptic equation with a logarithmic type perturbation
In this note, we consider a critical elliptic equation perturbed by a logarithmic type subcritical term in R4 , and investigate how the logarithmic term affects the existence of weak solutions to such a problem. Since the logarithmic term does not satisfy the standard monotonicity condition, essenti...
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: | Elliptikus egyenlet, Differenciálegyenlet - nemlineáris - parciális, Differenciálegyenlet - elliptikus, Sobolev-tér |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.5 |
| Online Access: | http://acta.bibl.u-szeged.hu/88885 |
| LEADER | 01707nas a2200241 i 4500 | ||
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| 024 | 7 | |a 10.14232/ejqtde.2025.1.5 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Li Haixia | |
| 245 | 1 | 2 | |a A critical elliptic equation with a logarithmic type perturbation |h [elektronikus dokumentum] / |c Li Haixia |
| 260 | |c 2025 | ||
| 300 | |a 12 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a In this note, we consider a critical elliptic equation perturbed by a logarithmic type subcritical term in R4 , and investigate how the logarithmic term affects the existence of weak solutions to such a problem. Since the logarithmic term does not satisfy the standard monotonicity condition, essential difficulty arises when one looks for weak solutions to this problem in the variational framework. After some delicate estimates on the logarithmic term we can control the mountain pass level of the corresponding functional so that it satisfies the local compactness condition. Then a positive weak solution follows with the application of the Mountain Pass Lemma and the Brézis–Lieb Lemma. Our result implies that the logarithmic term plays a positive role for the problem to admit positive solutions. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Elliptikus egyenlet, Differenciálegyenlet - nemlineáris - parciális, Differenciálegyenlet - elliptikus, Sobolev-tér | ||
| 700 | 0 | 1 | |a Han Yuzhu |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/88885/1/ejqtde_2025_005.pdf |z Dokumentum-elérés |