Navegar

Colección

Datos Estadísticas

Artículo

De Nápoli, P.L.; Bonder, J.F.; Silva, A. "Multiple solutions for the p-Laplace operator with critical growth" (2009) Nonlinear Analysis, Theory, Methods and Applications. 71(12):6283-6289
La versión final de este artículo es de uso interno. El editor solo permite incluir en el repositorio el artículo en su versión post-print. Por favor, si usted la posee enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation - Δp u = | u |p* - 2 u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂ Ω, where p* = N p / (N - p) is the critical Sobolev exponent and Δp u = div (| ∇ u |p - 2 ∇ u) is the p-Laplacian. The proof is based on variational arguments and the classical concentration compactness method. © 2009 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Multiple solutions for the p-Laplace operator with critical growth
Autor:De Nápoli, P.L.; Bonder, J.F.; Silva, A.
Filiación:Departamento de Matemática, FCEyN, UBA, 1428 Buenos Aires, Argentina
Palabras clave:Critical growth; p-Laplace equations; Variational methods; Bounded domain; Critical growth; Critical Sobolev exponent; Dirichlet boundary condition; Multiple solutions; Nontrivial solution; P-Laplace equations; P-Laplace operator; P-Laplacian; Quasilinear elliptic equations; Variational methods; Laplace transforms; Mathematical operators; Nonlinear equations; Laplace equation
Año:2009
Volumen:71
Número:12
Página de inicio:6283
Página de fin:6289
DOI: http://dx.doi.org/10.1016/j.na.2009.06.036
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6283_DeNapoli

Referencias:

  • Escobar, J.F., Uniqueness theorems on conformal deformations of metrics, Sobolev inequalities, and an eigenvalue estimate (1990) Comm. Pure Appl. Math., 43, pp. 857-883
  • Tolksdorf, P., Regularity for a more general class of quasilinear elliptic equations (1984) J. Differential Equations, 51, pp. 126-150
  • Arcoya, D., Diaz, J.I., S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology (1998) J. Differential Equations, 150, pp. 215-225
  • Atkinson, C., El Kalli, K., Some boundary value problems for the Bingham model (1992) J. Non-Newtonian Fluid Mech., 41, pp. 339-363
  • Atkinson, C., Champion, C.R., On some boundary value problems for the equation ∇ (F (| ∇ w |) ∇ w) = 0 (1995) Proc. R. Soc. London A, 448, pp. 269-279
  • Diaz, J.I., (1985) Nonlinear Partial Differential Equations and Free Boundaries, , Pitman Publ. Program
  • Struwe, M., Three nontrivial solutions of anticoercive boundary value problems for the Pseudo-Laplace operator (1981) J. Reine Angew. Math., 325, pp. 68-74
  • Fernández Bonder, J., Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities (2004) Abstr. Appl. Anal., 2004 (12), pp. 1047-1056
  • Rabinowitz, P., Minimax methods in critical point theory with applications to differential equations (1986) CBMS Regional Conf. Ser. in Math., 65. , Amer. Math. Soc., Providence, R.I
  • Dinca, G., Jebelean, P., Mawhin, J., Variational and Topological methods for Dirichlet Problems with p-Laplacian (2001) Port. Math., 58 (3), pp. 339-378
  • Schwartz, J.T., Generalizing the Lusternik-Schnirelman theory of critical points (1964) Comm. Pure Appl. Math., 17, pp. 307-315
  • Lions, P.L., The concentration-compactness principle in the calculus of variations. The limit case, part 1 (1985) Rev. Mat. Iberoamericana, 1 (1), pp. 145-201
  • Garcia-Azorero, J., Peral, I., Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term (1991) Trans. Amer. Math. Soc., 323 (2), pp. 877-895
  • Bartsch, T., Liu, Z., On a superlinear elliptic p-Laplacian equation (2004) J. Differential Equations, 198, pp. 149-175
  • Zhang, Z., Chen, J., Li, S., Construction of pseudo-gradient vector field and sign-changing multiple solutions involving p-Laplacian (2004) J. Differential Equations, 201, pp. 287-303
  • Guedda, M., Veron, L., Quasilinear elliptic equations involving critical Sobolev exponents (1989) Nonlinear Anal. TMA, 13, pp. 879-902
  • Cingolani, S., Vannella, G., Multiple positive solutions for a critical quasilinear equation via Morse theory (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2), pp. 397-413
  • Ekeland, I., On the variational principle (1974) J. Math. Anal. Appl., 47, pp. 324-353

Citas:

---------- APA ----------
De Nápoli, P.L., Bonder, J.F. & Silva, A. (2009) . Multiple solutions for the p-Laplace operator with critical growth. Nonlinear Analysis, Theory, Methods and Applications, 71(12), 6283-6289.
http://dx.doi.org/10.1016/j.na.2009.06.036
---------- CHICAGO ----------
De Nápoli, P.L., Bonder, J.F., Silva, A. "Multiple solutions for the p-Laplace operator with critical growth" . Nonlinear Analysis, Theory, Methods and Applications 71, no. 12 (2009) : 6283-6289.
http://dx.doi.org/10.1016/j.na.2009.06.036
---------- MLA ----------
De Nápoli, P.L., Bonder, J.F., Silva, A. "Multiple solutions for the p-Laplace operator with critical growth" . Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 12, 2009, pp. 6283-6289.
http://dx.doi.org/10.1016/j.na.2009.06.036
---------- VANCOUVER ----------
De Nápoli, P.L., Bonder, J.F., Silva, A. Multiple solutions for the p-Laplace operator with critical growth. Nonlinear Anal Theory Methods Appl. 2009;71(12):6283-6289.
http://dx.doi.org/10.1016/j.na.2009.06.036