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.
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.
Accepted:
Published online:
Anass Ourraoui 1
@article{CRMATH_2016__354_3_253_0, author = {Anass Ourraoui}, title = {On an elliptic equation of {\protect\emph{p}-Kirchhoff} type with convection term}, journal = {Comptes Rendus. Math\'ematique}, pages = {253--256}, publisher = {Elsevier}, volume = {354}, number = {3}, year = {2016}, doi = {10.1016/j.crma.2015.10.025}, language = {en}, }
Anass Ourraoui. On an elliptic equation of p-Kirchhoff type with convection term. Comptes Rendus. Mathématique, Volume 354 (2016) no. 3, pp. 253-256. doi : 10.1016/j.crma.2015.10.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.025/
[1] A sub-supersolution approach for a quasilinear Kirchhoff equation, J. Math. Phys., Volume 56 (2015)
[2] On some nonlocal problem involving the N-Laplacian in , Nonlinear Stud., Volume 22 (2015) no. 1, pp. 57-70
[3] Stationary Kirchhoff problems involving a fractional operator and a critical nonlinearity, Nonlinear Anal., Volume 125 (2015), pp. 699-714
[4] Positive solutions for p-Kirchhoff type problems on , Math. Methods Appl. Sci., Volume 38 (2015) no. 12, pp. 2650-2662
[5] 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] 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] 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] Topics in Functional Analysis and Applications, John Wiley & Sons, New York, 1989
[9] Mechanik, Teubner, Leipzig, Germany, 1883
[10] J. Liu, J.F. Liao, C.-L. Tang, Positive solutions for Kirchhoff-type equations with critical exponent in , J. Math. Anal. Appl 429 (2), 1153–1172.
[11] A. Ourraoui, On a class of nonlocal problem involving a critical exponent, preprint, 2015.
[12] Critical stationary Kirchhoff equations in involving nonlocal operators, Rev. Mat. Iberoam. (2016) (23 pp., in press)
Cited by Sources:
Comments - Policy