Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems
In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter $\lambda>0$ varies. In our first result, the superlinear perturbati...
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| Format: | Article |
| Language: | English |
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University of Szeged
2022-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9540 |
| _version_ | 1797830453269364736 |
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| author | Ricardo Alves |
| author_facet | Ricardo Alves |
| author_sort | Ricardo Alves |
| collection | DOAJ |
| description | In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter $\lambda>0$ varies. In our first result, the superlinear perturbation has an arbitrary growth and we obtain the existence of a solution for the problem by using the sub-supersolution method. For the second result, the superlinear perturbation has subcritical growth and we employ the Mountain Pass Theorem to show the existence of a second solution. |
| first_indexed | 2024-04-09T13:37:30Z |
| format | Article |
| id | doaj.art-9cffc764763041d6bcad1a4e145841b1 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:30Z |
| publishDate | 2022-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-9cffc764763041d6bcad1a4e145841b12023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752022-03-0120221312910.14232/ejqtde.2022.1.139540Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problemsRicardo Alves0Centro de Ciências exatas e Tecnológicas, Universidade Federal do Acre, BrazilIn the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter $\lambda>0$ varies. In our first result, the superlinear perturbation has an arbitrary growth and we obtain the existence of a solution for the problem by using the sub-supersolution method. For the second result, the superlinear perturbation has subcritical growth and we employ the Mountain Pass Theorem to show the existence of a second solution.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9540extended functionalsub-supersolution methodsingular problemvariational methods |
| spellingShingle | Ricardo Alves Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems Electronic Journal of Qualitative Theory of Differential Equations extended functional sub-supersolution method singular problem variational methods |
| title | Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems |
| title_full | Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems |
| title_fullStr | Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems |
| title_full_unstemmed | Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems |
| title_short | Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems |
| title_sort | existence nonexistence and multiplicity of positive solutions for singular quasilinear problems |
| topic | extended functional sub-supersolution method singular problem variational methods |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9540 |
| work_keys_str_mv | AT ricardoalves existencenonexistenceandmultiplicityofpositivesolutionsforsingularquasilinearproblems |