Artykuł
Study of fractional semipositone problems on RN
| creativeworkseries.issn | 1232-9274 | |
| dc.contributor.author | Biswas, Nirjan | |
| dc.date.issued | 2024 | |
| dc.description.abstract | Let $s\in (0,1)$ and $N\gt 2s$. In this paper, we consider the following class of nonlocal semipositone problems: $(-\Delta)^s u= g(x)f_a(u)\text{ in }\mathbb{R}^N,\quad u \gt 0\text{ in }\mathbb{R}^N,$ where the weight $g \in L^1(\mathbb{R}^N) \cap L^{\infty}(\mathbb{R}^N)$ is positive, $a\gt 0$ is a parameter, and $f_a \in \mathcal{C}(\mathbb{R})$ is strictly negative on $(-\infty,0]$. For $f_a$ having subcritical growth and weaker Ambrosetti-Rabinowitz type nonlinearity, we prove that the above problem admits a mountain pass solution $u_a$, provided a is near zero. To obtain the positivity of $u_a$, we establish a Brezis-Kato type uniform estimate of $(u_a)$ in $L^r(\mathbb{R}^N)$ for every $r \in [\frac{2N}{N-2s}, \infty]$. | en |
| dc.description.placeOfPublication | Kraków | |
| dc.description.version | wersja wydawnicza | |
| dc.identifier.doi | https://doi.org/10.7494/OpMath.2024.44.4.445 | |
| dc.identifier.eissn | 2300-6919 | |
| dc.identifier.issn | 1232-9274 | |
| dc.identifier.uri | https://repo.agh.edu.pl/handle/AGH/108410 | |
| dc.language.iso | eng | |
| dc.publisher | Wydawnictwa AGH | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.access | otwarty dostęp | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/legalcode | |
| dc.subject | semipositone problems | en |
| dc.subject | fractional operator | en |
| dc.subject | uniform regularity estimates | en |
| dc.subject | positive solutions | en |
| dc.title | Study of fractional semipositone problems on RN | en |
| dc.title.related | Opuscula Mathematica | |
| dc.type | artykuł | |
| dspace.entity.type | Publication | |
| publicationissue.issueNumber | No. 4 | |
| publicationissue.pagination | pp. 445-470 | |
| publicationvolume.volumeNumber | Vol. 44 | |
| relation.isJournalIssueOfPublication | 958a565f-0ba8-4db5-bbd6-a87484b6015d | |
| relation.isJournalIssueOfPublication.latestForDiscovery | 958a565f-0ba8-4db5-bbd6-a87484b6015d | |
| relation.isJournalOfPublication | 304b3b9b-59b9-4830-9178-93a77e6afbc7 |
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