Positive solutions for nonlinear Robin problems with conviction

• Autorzy: Gasiński Leszek , Papageorgiou Nikolaos S.

Identyfikatory

DOI

10.5604/01.3001.0015.2690

• Języki publikacji: EN

Abstrakty

EN

We consider a Robin problem driven by the p-Laplacian and with a reaction which is gradient dependent (convection). Using truncations and perturbations, we show that the problem has at least one positive smooth solution.

Słowa kluczowe

EN

convection; pseudo-monotone operator; strong comparison principle; nonlinear regularity

PL

konwekcja; operator pseudo-monotoniczny; zasada silnego porównania; regularność nieliniowa

• Wydawca: Państwowa Wyższa Szkoła Zawodowa w Tarnowie
• Czasopismo: Science, Technology and Innovation
• Rocznik: 2021
• Tom: Vol. 12, no. 1
• Strony: 23--36
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Gasiński Leszek

• University of Applied Sciences in Tarnow, Faculty of Mathematics and Natural Sicences, ul. Mickiewicza 8, 33-100 Tarnów, Poland

autor

Papageorgiou Nikolaos S.

• National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece

Bibliografia

• [1] Bai Y. Existence of solutions to nonhomogeneous Dirichlet problems with dependence on the gradient. Electronic Journal of Differential Equations. 2018;101:1–18.
• [2] Bai Y, Gasiński L, Papageorgiou NS. Nonlinear nonhomogeneous Robin problems with dependence on the gradient. Boundary Value Problems. 2018;17,1–24. doi: https://doi.org/10.1186/s13661-018-0936-8.
• [3] Faraci F, Motreanu D, Puglisi D. Positive solutions of quasi-linear elliptic equations with dependence on the gradient. Calculus of Variations and Partial Differential Equations. 2015;54(1):525–538. doi: https://doi.org/10.1007/s00526-014-0793-y.
• [4] Gasiński L, Krech I, Papageorgiou NS. Nonlinear nonhomogeneous Robin problems with gradient dependent reaction. Nonlinear Analysis. Real World Applications. 2020;55:103135. doi: https://doi.org/10.1016/j.nonrwa.2020.103135.
• [5] Gasiński L, Papageorgiou NS. Nonlinear analysis. Boca Raton: Chapman & Hall/CRC; 2006.
• [6] Gasiński L, Papageorgiou NS. Positive solutions for nonlinear elliptic problems with dependence on the gradient. Journal of Differential Equations. 2017;263(2):1451–1476. doi: https://doi.org/10.1016/j.jde.2017.03.021.
• [7] Lieberman GM. Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Analysis. Theory, Methods & Applications. 1988:12(11):1203–1219. doi: https://doi.org/10.1016/0362-546X(88)90053-3.
• [8] Papageorgiou NS, Rădulescu VD. Nonlinear nonhomogeneous Robin problems with superlinear reaction term. Advanced Nonlinear Studies. 2016;16(4):737–764. doi: https://doi.org/10.1515/ans-2016-0023.
• [9] Papageorgiou NS, RădulescuVD. Multiple solutions with precise sign for nonlinear parametric Robin problems. Journal of Differential Equations. 2014;256(7):2449–2479. doi: https://doi.org/10.1016/j.jde.2014.01.010.
• [10] Papageorgiou NS, Rădulescu VD, Repovš DD. Positive solutions for nonlinear nonhomogeneous parametric Robin problems. Forum Mathematicum. 2018;30(3):553–580. doi: https://doi.org/10.1515/forum-2017-0124.
• [11] Papageorgiou NS, Rădulescu VD, Repovš DD. Positive solutions for nonlinear Neumann problems with singular terms and Convection. Journal de Mathématiques Pures et Appliquées. 2020;136:1–21. doi: https://doi.org/10.1016/j.matpur.2020.02.004.
• [12] Zeng S, Papageorgiou NS. Positive solutions for (p, q)-equations with convection and a sign-changing reaction. Advances in Nonlinear Analysis. 2021;11(1):40–57. doi: https://doi.org/10.1515/anona-2020-0176.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).