Comptes Rendus
Ordinary differential equations/Partial differential equations
On a p-Kirchhoff problem involving a critical nonlinearity
Comptes Rendus. Mathématique, Volume 352 (2014) no. 4, pp. 295-298.

On s'intéresse dans cet article au problème de p-Kirchhoff à exposant critique. On montre l'existence d'au moins une solution sous des hypothèses adéquates.

This paper deals with a p-Kirchhoff type problem involving the critical Sobolev exponent. Under some suitable assumptions, we show the existence of at least one solution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.01.015
Anass Ourraoui 1

1 University Mohamed I, Faculty of Sciences, Department of Mathematics, Oujda, Morocco
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Anass Ourraoui. On a p-Kirchhoff problem involving a critical nonlinearity. Comptes Rendus. Mathématique, Volume 352 (2014) no. 4, pp. 295-298. doi : 10.1016/j.crma.2014.01.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.01.015/

[1] M. Allaoui; A. El Amrouss; A. Ourraoui On a class of nonlocal p(x)-Laplacian Neumann problems, Thai J. Math. (2014) (15 p.), in press

[2] C.O. Alves; F.J.S.A. Corrêa; G.M. Figueiredo On a class of nonlocal elliptic problems with critical growth, Differ. Equ. Appl., Volume 2 (2010), pp. 409-417

[3] G. Autuori; F. Colasuonno; P. Pucci Lifespan estimates for solutions of polyharmonic Kirchhoff systems, M3AS: Math. Models Methods Appl. Sci., Volume 22 (2012), p. 1150009 (36 p.)

[4] G. Autuori; F. Colasuonno; P. Pucci On the existence of stationary solutions for higher-order p-Kirchhoff problems, Commun. Contemp. Math. (2014) (33 p.), in press

[5] G. Autuori; P. Pucci Kirchhoff systems with dynamic boundary conditions, Nonlinear Anal., Volume 73 (2010), pp. 1952-1965

[6] G. Autuori; P. Pucci; M.C. Salvatori Global nonexistence for nonlinear Kirchhoff systems, Arch. Ration. Mech. Anal., Volume 196 (2010), pp. 489-516

[7] M. Chipot; B. Lovat Some remarks on nonlocal elliptic and parabolic problems, Nonlinear Anal., Volume 30 (1997) no. 7, pp. 4619-4627

[8] F. Colasuonno; P. Pucci Multiplicity of solutions for p(x)-polyharmonic elliptic Kirchhoff equations, Nonlinear Anal., Volume 74 (2011), pp. 5962-5974

[9] M. Dreher The Kirchhoff equation for the p-Laplacian, Rend. Semin. Mat. (Torino), Volume 64 (2006), pp. 217-238

[10] I. Ekeland On the variational principle, J. Math. Anal. Appl., Volume 47 (1974), pp. 324-353

[11] A. El Hamidi; J.M. Rakotoson Compactness and quasilinear problems with critical exponents, Differ. Integral Equ., Volume 18 (2005), pp. 1201-1220

[12] A. Fiscella, E. Valdinoci, A critical Kirchhoff type problem involving a non-local operator, preprint.

[13] A. Hamydy; M. Massar; N. Tsouli Existence of solutions for a p-Kirchhoff type problems with critical exponent, Electron. J. Differ. Equ., Volume 2011 (2011), pp. 1-8

[14] G. Kirchhoff Mechanik, Teubner, Leipzig, 1883

[15] J.-L. Lions On some questions in boundary value problems of mathematical physics, Rio de Janeiro, 1977 (G.M. De La Penha; L.A.J. Medeiros, eds.) (North-Holland Mathematics Studies), Volume vol. 30 (1978), pp. 284-346

[16] T.F. Ma Remarks on an elliptic equation of Kirchhoff type, Nonlinear Anal., Volume 63 (2005), pp. 1967-1977

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