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Abstrakty
In this paper, we prove some qualitative properties for the positive solutions to some degenerate elliptic equation given by [formula] on smooth domain and for varying nonlinearity ∫.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
483--494
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Aalto University Department of Mathematics and System Analysis Espoo-02150, Finland
Bibliografia
- [1] W. Allegretto, Y.X. Huang, A Picone's identity for the p-Laplacian and applications, Nonlinear Anal. 32 (1998) 7, 819-830.
- [2] K. Bal, Generalized Picone's identity and its applications, Electron. J. Differential Equations 2013 (2013) 243, 1-6.
- [3] K. Bal, Uniqueness of a positive solution for quasilinear elliptic equations in Heisenberg group, Electron. J. Differential Equations 2016 (2016) 130, 1-7.
- [4] K. Bal, P. Garain, I. Mandal, Some qualitative properties of Finsler p-Laplacian, Indag. Math. (N.S.) 28 (2017) 6, 1258-1264.
- [5] M. Belloni, B. Kawohl, A direct uniqueness proof for equations involving the p-Laplace operator, Manuscripta Math. 109 (2002) 2, 229-231.
- [6] S. Chanillo, R.L. Wheeden, Weighted Poincare and Sobolev inequalities and estimates for weighted Peano maximal functions, Amer. J. Math. 107 (1985) 5, 1191-1226.
- [7] V. De Cicco, M.A. Vivaldi, Weighted Poincare and Sobolev inequalities and estimates for weighted Peano maximal functions, Adv. Math. Sci. Appl. 9 (1999) 1, 183-207.
- [8] P. Drabek, A. Kufner, F. Nicolosi, Quasilinear elliptic equations with degenerations and singularities, De Gruyter Series in Nonlinear Analysis and Applications, vol. 5, Walter de Gruyter & Co., Berlin, 1997.
- [9] G. Dwivedi, J. Tyagi, Some qualitative questions on the equation — div(a(x,u, Vu)) = f{x,u), J. Math. Anal. Appl. 446 (2017) 1, 456-469.
- [10] E.B. Fabes, C.E. Kenig, R.P. Serapioni, The local regularity of solutions of degenerated elliptic equations, Commun. Partial Diff. Eq. 7 (1982) 1, 77-116.
- [11] J. Heinonen, T. Kilpelainen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993.
- [12] J. Jaros, Picone's identity for the p-biharmonic operator with applications, Electron. J. Differential Equations 2011 (2011) 122, 1-6.
- [13] J. Jaros, Generalized Picone identity and comparison of half-linear differential equations of order Am, Mem. Differ. Equ. Math. Phys. 57 (2012) 41-50.
- [14] J. Jaros, Picone's identity for a system, of first-order nonlinear partial differential equations, Electron. J. Differential Equations 2013 (2013) 143, 1-7.
- [15] J. Jaros, Picone's identity for a Finsler p-Laplacian and comparison of nonlinear elliptic equations, Math. Bohem. 139 (2014) 3, 535-552.
- [16] J. Jaros, A-harmonic Picone's identity with applications, Ann. Mat. Pura Appl. (4) 194 (2015) 3, 719-729.
- 17] J. Jaros, Caccioppoli estimates through an anisotropic Picone's identity, Proc. Amer. Math. Soc. 143 (2015) 3, 1137-1144.
- [18] J. Jaros, K. Takaśi, N. Yoshida, Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications, J. Inequal. Appl. (2006), 1-17.
- [19] B. Kawohl, M. Lucia, S. Prashanth, Simplicity of the principal eigenvalue for indefinite quasilinear problems, Adv. Differential Equations 12 (2007), 407-434.
- [20] J. Tyagi, A nonlinear Picone's identity and its applications, Appl. Math. Lett. 26 (2013) 6, 624-626.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
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