Positive solutions of an elliptic equation involving a sign-changing potential and a gradient term

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dc.citation.epage1118
dc.citation.issue4
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage1109
dc.contributor.affiliationУніверситет Абдельмалека Ессааді
dc.contributor.affiliationAbdelmalek Essaadi University
dc.contributor.authorБузелмат, А.
dc.contributor.authorЕль Багурі, Х.
dc.contributor.authorГміра, А.
dc.contributor.authorBouzelmate, A.
dc.contributor.authorEl Baghouri, H.
dc.contributor.authorGmira, A.
dc.coverage.placenameЛьвів
dc.date.accessioned2025-03-10T09:21:52Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractМетою цієї статті є дослідження еліптичного сингулярного рівняння Лапласа ∆u −|∇ u| q +up−u−δ = 0 в RN , де N > 1, 1 < q < p та δ > 2. Основний наш вклад полягає у встановленні існування строго додатного розв’язку та аналізі певних властивостей його асимптотичної поведінки, зокрема, коли він є монотонним.
dc.description.abstractThe objective of this paper is to investigate the elliptic singular Laplacian equation ∆u −|∇ u| q + up− u−δ = 0 in RN , where N > 1, 1 < q < p and δ > 2. Our main contributions consist of establishing the existence of an entire strictly positive solution and analyzing certain properties of its asymptotic behavior, particularly when it exhibits monotonicity.
dc.format.extent1109-1118
dc.format.pages10
dc.identifier.citationBouzelmate A. Positive solutions of an elliptic equation involving a sign-changing potential and a gradient term / A. Bouzelmate, H. El Baghouri, A. Gmira // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1109–1118.
dc.identifier.citationenBouzelmate A. Positive solutions of an elliptic equation involving a sign-changing potential and a gradient term / A. Bouzelmate, H. El Baghouri, A. Gmira // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1109–1118.
dc.identifier.doidoi.org/10.23939/mmc2023.04.1109
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/64063
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 4 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 4 (10), 2023
dc.relation.references[1] Serrin J., Zou H. Existence and nonexistence results for ground states of quasilinear elliptic equations. Archive for Rational Mechanics and Analysis. 121, 101–130 (1992).
dc.relation.references[2] Quittner Q. On global existence and stationary solutions for two classes of semilinear parabolic equations. Commentationes Mathematicae Universitatis Carolinae. 34 (1), 105–124 (1993).
dc.relation.references[3] Souplet P., Tayachi S., Weissler F. B. Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term. Indiana University Mathematics Journal. 45 (3), 655–682 (1996).
dc.relation.references[4] Souplet P. Recent results and open problems on parabolic. Electronic Journal of Differential Equations. 34, 105–124 (1993).
dc.relation.references[5] Bidaut-V`eron M.-F., V`eron L. Local behaviour of the solutions of the Chipot-Weissler equation. Preprint arXiv:2303.08074 (2023).
dc.relation.references[6] Gkikas K. T., Nguyen P.-T. Elliptic equations with Hardy potential and gradient-dependent nonlinearity. Advanced Nonlinear Studies. 20 (2), 399–435 (2020).
dc.relation.references[7] Gkikas K., Nguyen P.-T. Semilinear elliptic equations with Hardy potential and gradient nonlinearity. Revista Matem´atica Iberoamericana. 36 (4), 1207–1256 (2020).
dc.relation.references[8] Fowler R. H. The form near infinity of real continuos solutions of a certain differential equation of second order. Quarterly Journal of Mathematics. 45, 289–350 (1914).
dc.relation.references[9] Fowler R. H. The solutions of Emden’s and similar differential equation. Monthly Notices of the Royal Astronomical Society. 91 (1), 63–91 (1920).
dc.relation.references[10] Fowler R. H. Further studies on Emden’s and similar differential equation. Quarterly Journal of Mathematics. 2 (1), 259–288 (1931).
dc.relation.references[11] Lions P. L. Isolated singularities in semilinear problems. Journal of Differential Equations. 38 (3), 441–450 (1980).
dc.relation.references[12] Aviles P. Local behavior of positive solutions of some elliptic equation. Communications in Mathematical Physics. 108, 177–192 (1987).
dc.relation.references[13] Gidas B., Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Communications on Pure and Applied Mathematics. 34 (4), 525–598 (1980).
dc.relation.references[14] Caffarelli L. A., Gidas B., Spruck J. Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Communications on Pure and Applied Mathematics. 42, 271–297 (1989).
dc.relation.references[15] D`avila J., Montenegro M. Radial solutions of an elliptic equation with singular nonlinearity. Journal of Mathematical Analysis and Applications. 352 (1), 360–379 (2009).
dc.relation.references[16] Junping S., Miaoxin Y. On a singular nonlinear semilinear elliptic problem. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics. 128 (6), 1389–1401 (1998).
dc.relation.references[17] Ouyang T., Shi J., Yao M. Exact multiplicity and bifurcation of solutions of a singular equation. Preprint (1996).
dc.relation.references[18] Amann H. Ordinary Differential Equations. Walter de Gruyter, Belin, New York (1996).
dc.relation.references[19] Bouzelmate A., Gmira A., Reys G. On the Radial Solutions of a Degenerate Elliptic Equation with Convection Term. International Journal of Mathematical Analysis. 1 (20), 975–993 (2007).
dc.relation.references[20] Bouzelmate A., Gmira A. Singular solutions of an inhomogeneous elliptic equation. Nonlinear Functional Analysis and Applications. 26 (2), 237–272 (2021).
dc.relation.references[21] Ni W.-M., Serrin J. Nonexistence theorems for singular solutions of quasilinear partial differential equations. Communications on Pure and Applied Mathematics. 39 (3), 379–399 (1986).
dc.relation.referencesen[1] Serrin J., Zou H. Existence and nonexistence results for ground states of quasilinear elliptic equations. Archive for Rational Mechanics and Analysis. 121, 101–130 (1992).
dc.relation.referencesen[2] Quittner Q. On global existence and stationary solutions for two classes of semilinear parabolic equations. Commentationes Mathematicae Universitatis Carolinae. 34 (1), 105–124 (1993).
dc.relation.referencesen[3] Souplet P., Tayachi S., Weissler F. B. Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term. Indiana University Mathematics Journal. 45 (3), 655–682 (1996).
dc.relation.referencesen[4] Souplet P. Recent results and open problems on parabolic. Electronic Journal of Differential Equations. 34, 105–124 (1993).
dc.relation.referencesen[5] Bidaut-V`eron M.-F., V`eron L. Local behaviour of the solutions of the Chipot-Weissler equation. Preprint arXiv:2303.08074 (2023).
dc.relation.referencesen[6] Gkikas K. T., Nguyen P.-T. Elliptic equations with Hardy potential and gradient-dependent nonlinearity. Advanced Nonlinear Studies. 20 (2), 399–435 (2020).
dc.relation.referencesen[7] Gkikas K., Nguyen P.-T. Semilinear elliptic equations with Hardy potential and gradient nonlinearity. Revista Matem´atica Iberoamericana. 36 (4), 1207–1256 (2020).
dc.relation.referencesen[8] Fowler R. H. The form near infinity of real continuos solutions of a certain differential equation of second order. Quarterly Journal of Mathematics. 45, 289–350 (1914).
dc.relation.referencesen[9] Fowler R. H. The solutions of Emden’s and similar differential equation. Monthly Notices of the Royal Astronomical Society. 91 (1), 63–91 (1920).
dc.relation.referencesen[10] Fowler R. H. Further studies on Emden’s and similar differential equation. Quarterly Journal of Mathematics. 2 (1), 259–288 (1931).
dc.relation.referencesen[11] Lions P. L. Isolated singularities in semilinear problems. Journal of Differential Equations. 38 (3), 441–450 (1980).
dc.relation.referencesen[12] Aviles P. Local behavior of positive solutions of some elliptic equation. Communications in Mathematical Physics. 108, 177–192 (1987).
dc.relation.referencesen[13] Gidas B., Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Communications on Pure and Applied Mathematics. 34 (4), 525–598 (1980).
dc.relation.referencesen[14] Caffarelli L. A., Gidas B., Spruck J. Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Communications on Pure and Applied Mathematics. 42, 271–297 (1989).
dc.relation.referencesen[15] D`avila J., Montenegro M. Radial solutions of an elliptic equation with singular nonlinearity. Journal of Mathematical Analysis and Applications. 352 (1), 360–379 (2009).
dc.relation.referencesen[16] Junping S., Miaoxin Y. On a singular nonlinear semilinear elliptic problem. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics. 128 (6), 1389–1401 (1998).
dc.relation.referencesen[17] Ouyang T., Shi J., Yao M. Exact multiplicity and bifurcation of solutions of a singular equation. Preprint (1996).
dc.relation.referencesen[18] Amann H. Ordinary Differential Equations. Walter de Gruyter, Belin, New York (1996).
dc.relation.referencesen[19] Bouzelmate A., Gmira A., Reys G. On the Radial Solutions of a Degenerate Elliptic Equation with Convection Term. International Journal of Mathematical Analysis. 1 (20), 975–993 (2007).
dc.relation.referencesen[20] Bouzelmate A., Gmira A. Singular solutions of an inhomogeneous elliptic equation. Nonlinear Functional Analysis and Applications. 26 (2), 237–272 (2021).
dc.relation.referencesen[21] Ni W.-M., Serrin J. Nonexistence theorems for singular solutions of quasilinear partial differential equations. Communications on Pure and Applied Mathematics. 39 (3), 379–399 (1986).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectеліптичне рівняння
dc.subjectзнакозмінний потенціал
dc.subjectградієнтний член
dc.subjectрадіальний розв’язок
dc.subjectтеорема Банаха про нерухому точку
dc.subjectенергетична функція
dc.subjectосциляційні методи
dc.subjectelliptic equation
dc.subjectsign-changing potential
dc.subjectgradient term
dc.subjectradial solution
dc.subjectBanach fixed point theorem
dc.subjectenergy function
dc.subjectoscillation methods
dc.titlePositive solutions of an elliptic equation involving a sign-changing potential and a gradient term
dc.title.alternativeДодатні розв’язки еліптичного рівняння зі знакозмінним потенціалом та градієнтним членом
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 4