Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus

• Autorzy: Dridi S. , Khamessi B.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.l.21

• Języki publikacji: EN

Abstrakty

EN

In this paper, we establish existence and asymptotic behavior of a positive clas­sical solution to the following semilinear boundary value problem: [formula] Here O is an annulus in [formula] and q is a positive function in [formula], satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.

Słowa kluczowe

EN

asymptotic behavior; Dirichlet problem; Karamata function; subsolution; supersolution

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 1
• Strony: 21--36
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Dridi S.

• Campus Universitaire Faculte des Sciences de Tunis Departement de Mathematiques 2092 Tunis, Tunisia

autor

Khamessi B.

• Campus Universitaire Faculte des Sciences de Tunis Departement de Mathematiques 2092 Tunis, Tunisia

Bibliografia

• [1] D. Arcoya, Positive solutions for semilinear Dirichlet problems in an annulus, J. Dif­ferential Equations 94 (1991), 217-227.
• [2] S. Ben Othman, H. Maagli, S. Masmoudi, M. Zribi, Exat asymptotic behavior near the boundary to the solution for singular nonlinear Dirichlet problems, Nonlinear Anal. 71 (2009), 4137-4150.
• [3] F. Catrina, Nonexistence of positive radial solutions for a problem with singular poten­tial, Adv. Nonlinear Anal. 3 (2014) 1, 1-13.
• [4] A.B. Cavalheiro, Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations, Opuscula Math. 34 (2014) 1, 15-28.
• [5] R. Chemmam, H. Maagli, S. Masmoudi, M. Zribi, Combined effects in nonlinear singular-elliptic problems in a bounded domain, Adv. Nonlinear Anal. 1 (2012), 301-318.
• [6] R. Chemmam, A. Dhifli, H. Maagli, Asymptotic behavior of ground state solutions for semilinear and singular Dirichlet problem, Electron. J. Differential Equations 88 (2011), 1-12.
• [7] M.G. Crandall, P.H. Rabinowitz, L. Tartar, On a Dirichlet problem with a singular nonlinearity, Comm. Partial Differential Equations 2 (1977), 193-222.
• [8] X. Garaizar, Existence of positive radial solutions for semilinear elliptic equations in the annulus, J. Differential Equations 70 (1987), 69-92.
• [9] M. Ghergu, V.D. Radulescu, On a class of sublinear singular elliptic problems with convection term, J. Math. Anal. Appl. 311 (2005), 635-646.
• [10] M. Ghergu, V.D. Radulescu, Singular Elliptic Problems. Bifurcation and Asymptotic Analysis, Oxford Lecture Series in Mathematics and Applications, Vol. 37, Oxford Uni­versity Press, 2008, 320 pp.
• [11] M. Ghergu, V.D. Radulescu, Nonlinear PDEs Mathematical Models in Biology, Chem­istry and Population Genetics, Springer Monographs in Mathematics, Springer Verlag, 2012.
• [12] S. Gontara, H. Maagli, S. Masmoudi, S. Turki, Asymptotic behavior of positive solutions of a singular nonlinear Dirichlet problem, J. Math. Anal. Appl. 369 (2010), 719-729.
• [13] S. Jator, Z. Sinkala, Uniqueness of positive radial solutions for Am + f(u) = 0 in the annulus, Int. J. Pure Appl. Math. 12 (2004), 23-31.
• [14] H. Maagli, Asymptotic behavior of positive solutions of a semilinear Dirichlet problems, Nonlinear Anal. 74 (2011), 2941-2947.
• [15] H. Maagli, S. Turki, Z. Zine El Abidine, Asymptotic behavior of positive solutions of a semilinear Dirichlet problems outside the unit ball, Electron. J. Differential Equations 95 (2013), 1-14.
• [16] R. Seneta, Regular Varying Functions, Lecture Notes in Mathematics, Vol. 508, Springer-Verlag, Berlin, 1976.
• [17] M. Tang, Uniqueness of positive radial solutions for Am — u + up = 0 on an annulus, J. Differential Equations 189 (2003), 148-160.
• [18] Z. Zhang, The asymptotic behavior of the unique solution for the singular Lane-Emdem-Fowler equation, J. Math. Anal. Appl. 312 (2005), 33-43.
• [19] H. Wang, On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Differential Equations 109 (1994), 1-7.