Nonhomogeneous equations with critical exponential growth and lack of compactness
We study the existence and multiplicity of positive solutions for the following class of quasilinear problems \[-\operatorname{div}(a(|\nabla u|^{p})| \nabla u|^{p-2}\nabla u)+V(\epsilon x)b(|u|^{p})|u|^{p-2}u=f(u) \qquad\text{ in } \mathbb{R}^N,\] where \(\epsilon\) is a positive parameter. We assu...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2020-02-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol40/1/art/opuscula_math_4005.pdf |
| _version_ | 1818360939576033280 |
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| author | Giovany M. Figueiredo Vicenţiu D. Rădulescu |
| author_facet | Giovany M. Figueiredo Vicenţiu D. Rădulescu |
| author_sort | Giovany M. Figueiredo |
| collection | DOAJ |
| description | We study the existence and multiplicity of positive solutions for the following class of quasilinear problems \[-\operatorname{div}(a(|\nabla u|^{p})| \nabla u|^{p-2}\nabla u)+V(\epsilon x)b(|u|^{p})|u|^{p-2}u=f(u) \qquad\text{ in } \mathbb{R}^N,\] where \(\epsilon\) is a positive parameter. We assume that \(V:\mathbb{R}^N \to \mathbb{R}\) is a continuous potential and \(f:\mathbb{R}\to\mathbb{R}\) is a smooth reaction term with critical exponential growth. |
| first_indexed | 2024-12-13T21:08:46Z |
| format | Article |
| id | doaj.art-35e948de2b094afcbff3ff9596ed5697 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-13T21:08:46Z |
| publishDate | 2020-02-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-35e948de2b094afcbff3ff9596ed56972022-12-21T23:31:24ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742020-02-014017192https://doi.org/10.7494/OpMath.2020.40.1.714005Nonhomogeneous equations with critical exponential growth and lack of compactnessGiovany M. Figueiredo0https://orcid.org/0000-0003-1697-1592Vicenţiu D. Rădulescu1https://orcid.org/0000-0003-4615-5537Universidade de Brasília - UnB, Departamento de Matemàtica, CEP: 70910-900 Brasília-DF, BrazilAGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, PolandWe study the existence and multiplicity of positive solutions for the following class of quasilinear problems \[-\operatorname{div}(a(|\nabla u|^{p})| \nabla u|^{p-2}\nabla u)+V(\epsilon x)b(|u|^{p})|u|^{p-2}u=f(u) \qquad\text{ in } \mathbb{R}^N,\] where \(\epsilon\) is a positive parameter. We assume that \(V:\mathbb{R}^N \to \mathbb{R}\) is a continuous potential and \(f:\mathbb{R}\to\mathbb{R}\) is a smooth reaction term with critical exponential growth.https://www.opuscula.agh.edu.pl/vol40/1/art/opuscula_math_4005.pdfexponential critical growthquasilinear equationtrudinger-moser inequalitymoser iteration |
| spellingShingle | Giovany M. Figueiredo Vicenţiu D. Rădulescu Nonhomogeneous equations with critical exponential growth and lack of compactness Opuscula Mathematica exponential critical growth quasilinear equation trudinger-moser inequality moser iteration |
| title | Nonhomogeneous equations with critical exponential growth and lack of compactness |
| title_full | Nonhomogeneous equations with critical exponential growth and lack of compactness |
| title_fullStr | Nonhomogeneous equations with critical exponential growth and lack of compactness |
| title_full_unstemmed | Nonhomogeneous equations with critical exponential growth and lack of compactness |
| title_short | Nonhomogeneous equations with critical exponential growth and lack of compactness |
| title_sort | nonhomogeneous equations with critical exponential growth and lack of compactness |
| topic | exponential critical growth quasilinear equation trudinger-moser inequality moser iteration |
| url | https://www.opuscula.agh.edu.pl/vol40/1/art/opuscula_math_4005.pdf |
| work_keys_str_mv | AT giovanymfigueiredo nonhomogeneousequationswithcriticalexponentialgrowthandlackofcompactness AT vicentiudradulescu nonhomogeneousequationswithcriticalexponentialgrowthandlackofcompactness |