Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity
This paper deals with the existence of weak solutions to a Dirichlet problem for a semilinear elliptic equation involving the difference of two main nonlinearities functions that depends on a real parameter λ. According to the values of λ, we give both nonexistence and multiplicity results by using...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/6011860 |
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| _version_ | 1850176514735210496 |
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| author | Ayékotan Messan Joseph Tchalla Kokou Tcharie |
| author_facet | Ayékotan Messan Joseph Tchalla Kokou Tcharie |
| author_sort | Ayékotan Messan Joseph Tchalla |
| collection | DOAJ |
| description | This paper deals with the existence of weak solutions to a Dirichlet problem for a semilinear elliptic equation involving the difference of two main nonlinearities functions that depends on a real parameter λ. According to the values of λ, we give both nonexistence and multiplicity results by using variational methods. In particular, we first exhibit a critical positive value such that the problem admits at least a nontrivial non-negative weak solution if and only if λ is greater than or equal to this critical value. Furthermore, for λ greater than a second critical positive value, we show the existence of two independent nontrivial non-negative weak solutions to the problem. |
| format | Article |
| id | doaj-art-c1e34d2f6be34d459bb13c65cb397b1c |
| institution | OA Journals |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c1e34d2f6be34d459bb13c65cb397b1c2025-08-20T02:19:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/6011860Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric NonlinearityAyékotan Messan Joseph Tchalla0Kokou Tcharie1Département de MathématiquesDépartement de MathématiquesThis paper deals with the existence of weak solutions to a Dirichlet problem for a semilinear elliptic equation involving the difference of two main nonlinearities functions that depends on a real parameter λ. According to the values of λ, we give both nonexistence and multiplicity results by using variational methods. In particular, we first exhibit a critical positive value such that the problem admits at least a nontrivial non-negative weak solution if and only if λ is greater than or equal to this critical value. Furthermore, for λ greater than a second critical positive value, we show the existence of two independent nontrivial non-negative weak solutions to the problem.http://dx.doi.org/10.1155/2022/6011860 |
| spellingShingle | Ayékotan Messan Joseph Tchalla Kokou Tcharie Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity International Journal of Mathematics and Mathematical Sciences |
| title | Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity |
| title_full | Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity |
| title_fullStr | Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity |
| title_full_unstemmed | Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity |
| title_short | Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity |
| title_sort | multiplicity results for weak solutions of a semilinear dirichlet elliptic problem with a parametric nonlinearity |
| url | http://dx.doi.org/10.1155/2022/6011860 |
| work_keys_str_mv | AT ayekotanmessanjosephtchalla multiplicityresultsforweaksolutionsofasemilineardirichletellipticproblemwithaparametricnonlinearity AT kokoutcharie multiplicityresultsforweaksolutionsofasemilineardirichletellipticproblemwithaparametricnonlinearity |