Degenerate elliptic problem with singular gradient lower order term and variable exponents
| dc.citation.epage | 146 | |
| dc.citation.issue | 1 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 133 | |
| dc.contributor.affiliation | Алжирський університет | |
| dc.contributor.affiliation | University of Algiers | |
| dc.contributor.author | Зуатіні, М. А. | |
| dc.contributor.author | Мохтарі, Ф. | |
| dc.contributor.author | Хеліфі, Х. | |
| dc.contributor.author | Zouatini, M. A. | |
| dc.contributor.author | Mokhtari, F. | |
| dc.contributor.author | Khelifi, H. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T11:54:48Z | |
| dc.date.created | 2023-02-28 | |
| dc.date.issued | 2023-02-28 | |
| dc.description.abstract | У цій статті доводиться існування та регулярність слабких розв’язків для класу нелінійних еліптичних рівнянь із виродженою коерцитивною силою та сингулярними членами нижчого порядку з природним зростанням відносно за градієнтом і Lm(·)(m(x) > 1) даними. Функціональна постановка включає простори Лебега–Соболева зі змінними показниками. | |
| dc.description.abstract | In this paper, we prove the existence and regularity of weak solutions for a class of nonlinear elliptic equations with degenerate coercivity and singular lower-order terms with natural growth with respect to the gradient and Lm(·)(m(x) > 1) data. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. | |
| dc.format.extent | 133-146 | |
| dc.format.pages | 14 | |
| dc.identifier.citation | Zouatini M. A. Degenerate elliptic problem with singular gradient lower order term and variable exponents / M. A. Zouatini, F. Mokhtari, H. Khelifi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 133–146. | |
| dc.identifier.citationen | Zouatini M. A. Degenerate elliptic problem with singular gradient lower order term and variable exponents / M. A. Zouatini, F. Mokhtari, H. Khelifi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 133–146. | |
| dc.identifier.doi | 10.23939/mmc2023.01.133 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63485 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 1 (10), 2023 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 1 (10), 2023 | |
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| dc.relation.references | [9] Croce G. The regularizing effects of some lower order terms on the solutions in an elliptic equation with degenerate coercivity. Rendiconti di Matematica e delle sue Applicazioni. 27, 299–314 (2007). | |
| dc.relation.references | [10] Boccardo L. Quasilinear elliptic equations with natural growth terms: the regularizing effects of lower order terms. J. Nonlin. Conv. Anal. 7 (1), 355–365 (2006). | |
| dc.relation.references | [11] Croce G. An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term. Discrete and Continuous Dynamical Systems – S. 5 (3), 507–730 (2012). | |
| dc.relation.references | [12] Khelifi H. Existence and regularity for solution to a degenerate problem with singular gradient lower order term. Moroccan Journal of Pure and Applied Analysis. 8 (3), 310–327 (2022). | |
| dc.relation.references | [13] Carmona J., Mart´inez–Aparicio P. J., Rossi J. D. A singular elliptic equation with natural growth in the gradient and a variable exponent. Nonlinear Differential Equations and Applications. 22 (6), 1935–1948 (2015). | |
| dc.relation.references | [14] Fan X. L., Shen J., Zhao D. Sobolev embedding theorems for spaces W m,p(x) (Ω). Journal of Mathematical Analysis and Applications. 262 (2), 749–760 (2001). | |
| dc.relation.references | [15] Diening L., Harjulehto T., H¨ast¨o P., Ruzicka M. Lebesque and Sobolev spaces with variable exponents. Lecture Notes in Mathematics, Vol. 2017. Springer Verlag, Berlin (2011). | |
| dc.relation.references | [16] Carmona J., Mart´inez–Aparicio P. J., Su´arez A. Existence and nonexistence of positive solutions for nonlinear elliptic singular equations with natural growth. Nonlinear Analysis: Theory, Methods & Applications. 89, 157–169 (2013). | |
| dc.relation.references | [17] Arcoya D., Boccardo L., Leonori T., Porretta A. Some elliptic problems with singular natural growth lower order terms. Journal of Differential Equations. 249 (11), 2771–2795 (2010). | |
| dc.relation.references | [18] Carmona J., Mart´inez–Aparicio P. J. A Singular Semilinear Elliptic Equation with a Variable Exponent. Advanced Nonlinear Studies. 16 (3), 1935–1948 (2016). | |
| dc.relation.references | [19] Murat F., Bensoussan A., Boccardo L. On a nonlinear partial differential equation having natural growth terms and unbounded solutions. Annales de l’Institut Henri Poincar´e. Analyse Non Lin´eaire. 5 (4), 347–364 (1988). | |
| dc.relation.references | [20] Boccardo L., Murat F., Puel J.-P. L∞ estimate for some nonlinear elliptic partial differential equations and application to an existence result. SIAM Journal on Mathematical Analysis. 23 (2), 326–333 (1992). | |
| dc.relation.references | [21] Lions J. L. Quelques m´ethodes de r´esolution des probl`eemes aux limites. Dunod. Paris (1969). | |
| dc.relation.references | [22] Zhang Q. A strong maximum principle for differential equations with nonstandard p(x)-growth conditions. Journal of Mathematical Analysis and Applications. 312 (1), 24–32 (2005). | |
| dc.relation.references | [23] Wolanski N. Local bounds, Harnack’s inequality and H¨older continuity for divergence type elliptic equations with non-standard growth. Revista De La Uni´on Matem´atica Argentina. 56 (1), 73–105 (2015). | |
| dc.relation.referencesen | [1] Arcoya D., Barile S., Mart´inez–Aparicio P. J. Singular quasilinear equations with quadratic growth in the gradient without sign condition. Journal of Mathematical Analysis and Applications. 350 (1), 401–408 (2009). | |
| dc.relation.referencesen | [2] Boccardo L. Problems with singular and quadratic gradient lower order terms. ESAIM: Control, Optimisation and Calculus of Variations. 14 (3), 411–426 (2008). | |
| dc.relation.referencesen | [3] Giachetti D., Murat F. An elliptic problem with a lower order term having singular behaviour. Bollettino Della Unione Matematica Italiana. 2, 349–370 (2009). | |
| dc.relation.referencesen | [4] Khelifi H., Elhadfi Y. Nonlinear elliptic equations with variable exponents involving singular nonlinearity. Mathematical Modeling and Computing. 8 (4), 705–715 (2021). | |
| dc.relation.referencesen | [5] Zhan C. Entropy solutions for nonlinear elliptic equations with variable exponents. Electronic Journal of Differential Equations. 2014 (92), 1–14 (2014). | |
| dc.relation.referencesen | [6] Alvino A., Boccardo L., Ferone V., Orsina L., Trombetti G. Existence results for nonlinear elliptic equations with degenerate coercivity. Annali di Matematica Pura ed Applicata. 182 (1), 53–79 (2003). | |
| dc.relation.referencesen | [7] Boccardo L., Dall’ Aglio A., Orsina L. Existence and regularity results for some elliptic equations with degenerate coercivity. Atti Sem. Mat. Fis. Univ. Modena. 46, 51–81 (1998). | |
| dc.relation.referencesen | [8] Boccardo L. Some elliptic problems with degenerate coercivity. Advanced Nonlinear Studies. 6 (1), 1–12 (2006). | |
| dc.relation.referencesen | [9] Croce G. The regularizing effects of some lower order terms on the solutions in an elliptic equation with degenerate coercivity. Rendiconti di Matematica e delle sue Applicazioni. 27, 299–314 (2007). | |
| dc.relation.referencesen | [10] Boccardo L. Quasilinear elliptic equations with natural growth terms: the regularizing effects of lower order terms. J. Nonlin. Conv. Anal. 7 (1), 355–365 (2006). | |
| dc.relation.referencesen | [11] Croce G. An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term. Discrete and Continuous Dynamical Systems – S. 5 (3), 507–730 (2012). | |
| dc.relation.referencesen | [12] Khelifi H. Existence and regularity for solution to a degenerate problem with singular gradient lower order term. Moroccan Journal of Pure and Applied Analysis. 8 (3), 310–327 (2022). | |
| dc.relation.referencesen | [13] Carmona J., Mart´inez–Aparicio P. J., Rossi J. D. A singular elliptic equation with natural growth in the gradient and a variable exponent. Nonlinear Differential Equations and Applications. 22 (6), 1935–1948 (2015). | |
| dc.relation.referencesen | [14] Fan X. L., Shen J., Zhao D. Sobolev embedding theorems for spaces W m,p(x) (Ω). Journal of Mathematical Analysis and Applications. 262 (2), 749–760 (2001). | |
| dc.relation.referencesen | [15] Diening L., Harjulehto T., H¨ast¨o P., Ruzicka M. Lebesque and Sobolev spaces with variable exponents. Lecture Notes in Mathematics, Vol. 2017. Springer Verlag, Berlin (2011). | |
| dc.relation.referencesen | [16] Carmona J., Mart´inez–Aparicio P. J., Su´arez A. Existence and nonexistence of positive solutions for nonlinear elliptic singular equations with natural growth. Nonlinear Analysis: Theory, Methods & Applications. 89, 157–169 (2013). | |
| dc.relation.referencesen | [17] Arcoya D., Boccardo L., Leonori T., Porretta A. Some elliptic problems with singular natural growth lower order terms. Journal of Differential Equations. 249 (11), 2771–2795 (2010). | |
| dc.relation.referencesen | [18] Carmona J., Mart´inez–Aparicio P. J. A Singular Semilinear Elliptic Equation with a Variable Exponent. Advanced Nonlinear Studies. 16 (3), 1935–1948 (2016). | |
| dc.relation.referencesen | [19] Murat F., Bensoussan A., Boccardo L. On a nonlinear partial differential equation having natural growth terms and unbounded solutions. Annales de l’Institut Henri Poincar´e. Analyse Non Lin´eaire. 5 (4), 347–364 (1988). | |
| dc.relation.referencesen | [20] Boccardo L., Murat F., Puel J.-P. L∞ estimate for some nonlinear elliptic partial differential equations and application to an existence result. SIAM Journal on Mathematical Analysis. 23 (2), 326–333 (1992). | |
| dc.relation.referencesen | [21] Lions J. L. Quelques m´ethodes de r´esolution des probl`eemes aux limites. Dunod. Paris (1969). | |
| dc.relation.referencesen | [22] Zhang Q. A strong maximum principle for differential equations with nonstandard p(x)-growth conditions. Journal of Mathematical Analysis and Applications. 312 (1), 24–32 (2005). | |
| dc.relation.referencesen | [23] Wolanski N. Local bounds, Harnack’s inequality and H¨older continuity for divergence type elliptic equations with non-standard growth. Revista De La Uni´on Matem´atica Argentina. 56 (1), 73–105 (2015). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2023 | |
| dc.subject | вироджена задача | |
| dc.subject | сингулярний член | |
| dc.subject | регулярний розв’язок | |
| dc.subject | принцип порівняння | |
| dc.subject | нерівність Гарнака | |
| dc.subject | generate problem | |
| dc.subject | singular term | |
| dc.subject | regularity solution | |
| dc.subject | the comparison principle | |
| dc.subject | Harnack inequality | |
| dc.title | Degenerate elliptic problem with singular gradient lower order term and variable exponents | |
| dc.title.alternative | Вироджена еліптична задача зі сингулярним градієнтом нижчого порядку та змінним показником | |
| dc.type | Article |
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