no. 3
Ordinary differential equations/Partial differential equations
On an elliptic equation of p-Kirchhoff type with convection term

Présenté par : the Editorial Board

Ourraoui, Anass1
1 University Mohamed I, ENSAH, Department of Mathematics, Oujda, Morocco
Comptes Rendus. Mathématique, Tome 354 (2016) no. 3, pp. 253-256.

Dans ce travail, on utilise la méthode de Galerkin avec une estimation a priori pour montrer l'existence de solutions à une classe de problèmes elliptiques, donnée par un système d'équations non linéaires de type p-Kirchhoff en présence d'un terme de gradient.

In this paper, by using Galerkin's approach with a priori estimates, we establish the existence of solutions to a class of elliptic problems given by a system of nonlinear equations of p-Kirchhoff type with a convection term.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.10.025
Ourraoui, Anass 1

1 University Mohamed I, ENSAH, Department of Mathematics, Oujda, Morocco 
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Ourraoui, Anass. On an elliptic equation of p-Kirchhoff type with convection term. Comptes Rendus. Mathématique, Tome 354 (2016) no. 3, pp. 253-256. doi : 10.1016/j.crma.2015.10.025. http://www.numdam.org/articles/10.1016/j.crma.2015.10.025/

[1] Alves, C.O.; Correa, Francisco Julio S.A. A sub-supersolution approach for a quasilinear Kirchhoff equation, J. Math. Phys., Volume 56 (2015)

[2] Aouaoui, S. On some nonlocal problem involving the N-Laplacian in RN, Nonlinear Stud., Volume 22 (2015) no. 1, pp. 57-70

[3] Autuori, G.; Fiscella, A.; Pucci, P. Stationary Kirchhoff problems involving a fractional operator and a critical nonlinearity, Nonlinear Anal., Volume 125 (2015), pp. 699-714

[4] Cheng, X.; Dai, G. Positive solutions for p-Kirchhoff type problems on RN, Math. Methods Appl. Sci., Volume 38 (2015) no. 12, pp. 2650-2662

[5] Faria, L.F.O.; Miyagaki, O.H.; Pereira, F.R. Existence results for quasilinear elliptic exterior problems involving convection term and nonlinear Robin boundary conditions, J. Math. Anal. Appl., Volume 368 (2010), pp. 578-586

[6] Figueiredo, M.G. Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument, J. Math. Anal. Appl., Volume 401 (2013), pp. 706-713

[7] Figueiredo, G.M.; Santos, Jefferson A. On a Φ-Kirchhoff multivalued problem with critical growth in an Orlicz–Sobolev space, Asymptot. Anal., Volume 89 (2014) no. 1–2, pp. 151-172

[8] Kesavan, S. Topics in Functional Analysis and Applications, John Wiley & Sons, New York, 1989

[9] Kirchhoff, G. Mechanik, Teubner, Leipzig, Germany, 1883

[10] J. Liu, J.F. Liao, C.-L. Tang, Positive solutions for Kirchhoff-type equations with critical exponent in RN, J. Math. Anal. Appl 429 (2), 1153–1172.

[11] A. Ourraoui, On a class of nonlocal problem involving a critical exponent, preprint, 2015.

[12] Pucci, P.; Saldi, S. Critical stationary Kirchhoff equations in RN involving nonlocal operators, Rev. Mat. Iberoam. (2016) (23 pp., in press)

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