Nonlinear elliptic equations with variable exponents involving singular nonlinearity

Simple item page
dc.citation.epage715
dc.citation.issue4
dc.citation.spage705
dc.contributor.affiliationАлжирський університет
dc.contributor.affiliationМохтарський університет
dc.contributor.affiliationУніверситет Султана Мулая Слімана
dc.contributor.affiliationUniversity of Algiers
dc.contributor.affiliationBadji Mokhtar University
dc.contributor.affiliationSultan Moulay Slimane University
dc.contributor.authorХеліфі, Г.
dc.contributor.authorЕль Гадфі, Й.
dc.contributor.authorKhelifi, H.
dc.contributor.authorEl Hadfi, Y.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-11-01T07:49:21Z
dc.date.available2023-11-01T07:49:21Z
dc.date.created2021-03-01
dc.date.issued2021-03-01
dc.description.abstractУ статті доводиться існування та регулярність слабких додатних розв’язків для класу нелінійних еліптичних рівнянь із нелінійною сингулярністю, членами нижчого порядку та L1 в заданні просторів Соболєва зі змінними показниками. Доведено, що член нижчого порядку має деякий регуляризуючий вплив на розв’язок. Ця робота узагальнює деякі результати, наведені в [1–3]
dc.description.abstractIn this paper, we prove the existence and regularity of weak positive solutions for a class of nonlinear elliptic equations with a singular nonlinearity, lower order terms and L1 datum in the setting of Sobolev spaces with variable exponents. We will prove that the lower order term has some regularizing effects on the solutions. This work generalizes some results given in [1–3].
dc.format.extent705-715
dc.format.pages11
dc.identifier.citationKhelifi H. Nonlinear elliptic equations with variable exponents involving singular nonlinearity / H. Khelifi, Y. El Hadfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 4. — P. 705–715.
dc.identifier.citationenKhelifi H. Nonlinear elliptic equations with variable exponents involving singular nonlinearity / H. Khelifi, Y. El Hadfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 4. — P. 705–715.
dc.identifier.doi10.23939/mmc2021.04.705
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60435
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 4 (8), 2021
dc.relation.references[1] Boccardo L., Croce G. The impact of a lower order term in a Dirichlet problem with a singular nonlinearity. Portugaliae Mathematica. 76 (3–4), 4075 (2019).
dc.relation.references[2] Oliva F. Regularizing effect of absorption terms in singular problems. Journal of Mathematical Analysis and Applications. 472 (1), (2019).
dc.relation.references[3] Sbai A., El Hadfi Y. Regularizing effect of absorption terms in singular and degenerate elliptic problems. arXiv preprint arXiv:2008.03597 (2020).
dc.relation.references[4] Callegari A., Nashman A. A nonlinear singular boundary-value problem in the theory of pseudoplastic fluids. SIAM J. Appl. Math. 38, 275–281 (1980).
dc.relation.references[5] Keller H. B., Chohen D. S. Some positive problems suggested by nonlinear heat generators. Indiana Univ. Math. J. 16 (12), 1361–1376 (1967).
dc.relation.references[6] Ambrosetti A., Br´ezis H., Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J. Funct. Anal. 122 (2), 519–543 (1994).
dc.relation.references[7] El Ouardy M., El Hadfi Y., Ifzarne A. Existence and regularity results for a singular parabolic equations with degenerate coercivity. Discrete & Continuous Dynamical Systems – S. 1–25 (2021).
dc.relation.references[8] Sbai A., El Hadfi Y. Degenerate elliptic problem with a singular nonlinearity. arXiv e-prints arXiv:2005.08383 (2020).
dc.relation.references[9] Canino A., Sciunzi B., Trombetta A. Existence and uniqueness for p-Laplace equations involving singular nonlinearities. Nonlinear Differential Equations and Applications. 23, Article number: 8 (2016).
dc.relation.references[10] De Cave L M., Oliva F. On the regularizing effect of some absorption and singular lower order terms in classical Dirichlet problem with L1 data. Journal of Elliptic and Parabolic Equations. 2, 73–85 (2016).
dc.relation.references[11] Chu Y., Gao R., Sun Y. Existence and regularity of solutions to a quasilinear elliptic problem involving variable sources. Boundary Value Problems. 2017, Article number: 1 (2017).
dc.relation.references[12] Fan X., Zhao D. On the spaces Lp(x)(Ω) and W m,p(x)(Ω). Journal of Mathematical Analysis and Applications. 263 (2), 424–446 (2001).
dc.relation.references[13] Kov´aˆcik O., R`akosn´ik J. On spaces Lp(x)(Ω) and Wk,p(x)(Ω). Czechoslovak Mathematical Journal. 41 (4), 592–618 (1991).
dc.relation.references[14] Diening L., Harjulehto P., H¨ast¨o P., Ruzicka M. Lebesgue and Sobolev spaces with variable exponents. Lecture notes in mathematics. Heidelberg, Springer (2017).
dc.relation.references[15] R ˙uˇziˇcka M. Electrorheological fluids: modeling and mathematical theory. Lecture notes in mathematics. Berlin, Springer-Verlag (2000).
dc.relation.references[16] Carmona J., Marti´ınez-Aparicio Pedro J., Rossi Julio 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[17] Fan X. Positive solution to p(x)-Laplacian Dirichlet problems with sign-changing non-linearities. Glasgow Mathematical Journal. 52 (3), 505–516 (2010).
dc.relation.references[18] Papageorgiou N. S., Winkert P. Applied Nonlinear Functional Analysis. De Gruyter, Berlin (2018).
dc.relation.references[19] Papageorgiou N. S., R˘adulescu V. D., Repovˇs D. D. Nonlinear Analysis – Theory and Methods. Springer, Cham (2019).
dc.relation.references[20] Brezis H. Analyse fonctionnelle theorie et applications. New York, Springer (2010).
dc.relation.references[21] Stampacchia G. Le probl`eme de Dirichlet pour les ´equations elliptiques du second ordre `a coefficients discontinus. Annales de l’Institut Fourier. 15 (1), 189–257 (1965).
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.referencesen[1] Boccardo L., Croce G. The impact of a lower order term in a Dirichlet problem with a singular nonlinearity. Portugaliae Mathematica. 76 (3–4), 4075 (2019).
dc.relation.referencesen[2] Oliva F. Regularizing effect of absorption terms in singular problems. Journal of Mathematical Analysis and Applications. 472 (1), (2019).
dc.relation.referencesen[3] Sbai A., El Hadfi Y. Regularizing effect of absorption terms in singular and degenerate elliptic problems. arXiv preprint arXiv:2008.03597 (2020).
dc.relation.referencesen[4] Callegari A., Nashman A. A nonlinear singular boundary-value problem in the theory of pseudoplastic fluids. SIAM J. Appl. Math. 38, 275–281 (1980).
dc.relation.referencesen[5] Keller H. B., Chohen D. S. Some positive problems suggested by nonlinear heat generators. Indiana Univ. Math. J. 16 (12), 1361–1376 (1967).
dc.relation.referencesen[6] Ambrosetti A., Br´ezis H., Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J. Funct. Anal. 122 (2), 519–543 (1994).
dc.relation.referencesen[7] El Ouardy M., El Hadfi Y., Ifzarne A. Existence and regularity results for a singular parabolic equations with degenerate coercivity. Discrete & Continuous Dynamical Systems – S. 1–25 (2021).
dc.relation.referencesen[8] Sbai A., El Hadfi Y. Degenerate elliptic problem with a singular nonlinearity. arXiv e-prints arXiv:2005.08383 (2020).
dc.relation.referencesen[9] Canino A., Sciunzi B., Trombetta A. Existence and uniqueness for p-Laplace equations involving singular nonlinearities. Nonlinear Differential Equations and Applications. 23, Article number: 8 (2016).
dc.relation.referencesen[10] De Cave L M., Oliva F. On the regularizing effect of some absorption and singular lower order terms in classical Dirichlet problem with L1 data. Journal of Elliptic and Parabolic Equations. 2, 73–85 (2016).
dc.relation.referencesen[11] Chu Y., Gao R., Sun Y. Existence and regularity of solutions to a quasilinear elliptic problem involving variable sources. Boundary Value Problems. 2017, Article number: 1 (2017).
dc.relation.referencesen[12] Fan X., Zhao D. On the spaces Lp(x)(Ω) and W m,p(x)(Ω). Journal of Mathematical Analysis and Applications. 263 (2), 424–446 (2001).
dc.relation.referencesen[13] Kov´aˆcik O., R`akosn´ik J. On spaces Lp(x)(Ω) and Wk,p(x)(Ω). Czechoslovak Mathematical Journal. 41 (4), 592–618 (1991).
dc.relation.referencesen[14] Diening L., Harjulehto P., H¨ast¨o P., Ruzicka M. Lebesgue and Sobolev spaces with variable exponents. Lecture notes in mathematics. Heidelberg, Springer (2017).
dc.relation.referencesen[15] R ˙uˇziˇcka M. Electrorheological fluids: modeling and mathematical theory. Lecture notes in mathematics. Berlin, Springer-Verlag (2000).
dc.relation.referencesen[16] Carmona J., Marti´ınez-Aparicio Pedro J., Rossi Julio 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[17] Fan X. Positive solution to p(x)-Laplacian Dirichlet problems with sign-changing non-linearities. Glasgow Mathematical Journal. 52 (3), 505–516 (2010).
dc.relation.referencesen[18] Papageorgiou N. S., Winkert P. Applied Nonlinear Functional Analysis. De Gruyter, Berlin (2018).
dc.relation.referencesen[19] Papageorgiou N. S., R˘adulescu V. D., Repovˇs D. D. Nonlinear Analysis – Theory and Methods. Springer, Cham (2019).
dc.relation.referencesen[20] Brezis H. Analyse fonctionnelle theorie et applications. New York, Springer (2010).
dc.relation.referencesen[21] Stampacchia G. Le probl`eme de Dirichlet pour les ´equations elliptiques du second ordre `a coefficients discontinus. Annales de l’Institut Fourier. 15 (1), 189–257 (1965).
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.rights.holder© Національний університет “Львівська політехніка”, 2021
dc.subjectпростори Соболєва зі змінними показниками
dc.subjectсингулярна нелінійність
dc.subjectеліптичне рівняння
dc.subjectSobolev spaces with variable exponents
dc.subjectsingular nonlinearity
dc.subjectelliptic equation
dc.titleNonlinear elliptic equations with variable exponents involving singular nonlinearity
dc.title.alternativeНелінійні еліптичні рівняння зі змінними показниками, що включають сингулярну нелінійність
dc.typeArticle

Files

Original bundle

Now showing 1 - 2 of 2
Thumbnail Image
Name:
2021v8n4_Khelifi_H-Nonlinear_elliptic_equations_705-715.pdf
Size:
1.54 MB
Format:
Adobe Portable Document Format
Download
Thumbnail Image
Name:
2021v8n4_Khelifi_H-Nonlinear_elliptic_equations_705-715__COVER.png
Size:
271.57 KB
Format:
Portable Network Graphics
Download

License bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
1.79 KB
Format:
Plain Text
Description:
Download

Collections

Mathematical Modeling And Computing. – 2021. – Vol. 8, No. 4