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Abstract:

In this paper we study the existence of nontrivial solutions for the problem Δpu = up-2u in a bounded smooth domain Ω ⊂ ℝN, with a nonlinear boundary condition given by |∇u|p-2∂u/∂v = f(u) on the boundary of the domain. The proofs are based on variational and topological arguments. © 2001 Academic Press.

Registro:

Documento: Artículo
Título:Existence results for the p-Laplacian with nonlinear boundary conditions
Autor:Bonder, J.F.; Rossi, J.D.
Filiación:Departamento De Matemática, FCEyN UBA, 1428, Buenos Aires, Argentina
Palabras clave:Nonlinear boundary conditions; p-Laplacian
Año:2001
Volumen:263
Número:1
Página de inicio:195
Página de fin:223
DOI: http://dx.doi.org/10.1006/jmaa.2001.7609
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v263_n1_p195_Bonder.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v263_n1_p195_Bonder

Referencias:

  • Ambrosetti, A., Rabinowitz, P.H., Dual variational methods in critical point theory and applications (1973) J. Funct. Anal, 14, pp. 349-381. , No. 4
  • Babuska, I., Osborn, J., Eigenvalue problems (1991) "Handbook of Numerical Analysis", 2. , North-Holland, Amsterdam
  • Brezis, H., Niremberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents (1983) Comm. Pure Appl. Math, 36, pp. 437-477
  • Chabrowski, J., Yang, J., Existence theorems for elliptic equations involving supercritical Sobolev exponents (1997) Adv. Differential Equations, 2, pp. 231-256. , No. 2
  • Cherrier, P., Problèmes de Neumann non linéaires sur les variétés Riemanniennes (1984) J. Funct. Anal, 57, pp. 154-206
  • St. Cîrstea, F.-C., Radulescu, V., Existence and non-existence results for a quasilinear problem with nonlinear boundary conditions (2000) J. Math. Anal. Appl, 244, pp. 169-183
  • Chipot, M., Shafrir, I., Fila, M., On the solutions to some elliptic equations with nonlinear boundary conditions (1996) Adv. Differential Equations, 1, pp. 91-110. , No. 1
  • Chipot, M., Chlebík, M., Fila, M., Shafrir, I., Existence of positive solutions of a semilinear elliptic equation in δrN + with a nonlinear boundary condition (1998) J. Math. Anal. Appl, 223, pp. 429-471
  • Coffman, C.V., A minimum-maximum principle for a class of nonlinear integral equations (1969) J. Anal. Math, 22, pp. 391-419
  • Flores, C., Del Pino, M., Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains Comm. Partial Differential Equations, , to appear
  • 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
  • Escobar, J.F., Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature (1992) Ann. of Math, 136 (2), pp. 1-50
  • Fernández Bonder, J., Pinasco, J.P., Rossi, J.D., Existence results for a Hamiltonian elliptic system with nonlinear boundary conditions, Electron (1999) J. Differential Equations, pp. 1-15. , No. 40 1999
  • Fernández Bonder, J., Rossi, J.D., Existence for an elliptic system with nonlinear boundary conditions via fixed point methods (2001) Adv. Differential Equations, 6, pp. 1-20. , No. 1
  • 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, pp. 877-895. , No. 2
  • Garcia-Azorero, J., Peral, I., Existence and non-uniqueness for the p-Laplacian: Nonlinear eigenvalues (1987) Comm. Partial Differential Equations, 12, pp. 1389-1430
  • Hu, B., Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition (1994) Differential Integral Equations, 7, pp. 301-313. , No. 2
  • Krasnoselski, M.A., (1964) "Topological Methods in the Theory of Nonlinear Integral Equations", , MacMillan, New York
  • Lions, P.L., The concentration-compactness principle in the calculus of variations (1985) Rev. Mat. Iberoamericana, 1 (PART 1), pp. 145-201. , The limit case, No. 1
  • Lions, P.L., The concentration-compactness principle in the calculus of variations (1985) Rev. Mat. Iberoamericana, 1 (PART 2), pp. 45-121. , No. 2 The limit case
  • Montenegro, M., Montenegro, M., Existence and nonexistence of solutions for quasi-linear elliptic equations (2000) J. Math. Anal. Appl, 245, pp. 303-316
  • Pflüger, K., Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition (1998) Electron. J. Differential Equations, 10, pp. 1-13
  • Rabinowitz, P., "Minimax Methods in Critical Point Theory with Applications to Differential Equations" (1986) Amer. Math. Soc, , CBMS Regional Conference Series in Mathematics, no. 65, Providence
  • Simon, J., Regularité de la solution d'un problème aux limites non linéaires (1981) Ann. Fac. Sci. Toulouse Math, 3 (6), pp. 247-274
  • Terraccini, S., Symmetry properties of positive solutions to some alliptic equations with nonlinear boundary conditions (1995) Differential Integral Equations, 8, pp. 1911-1922. , No. 8

Citas:

---------- APA ----------
Bonder, J.F. & Rossi, J.D. (2001) . Existence results for the p-Laplacian with nonlinear boundary conditions. Journal of Mathematical Analysis and Applications, 263(1), 195-223.
http://dx.doi.org/10.1006/jmaa.2001.7609
---------- CHICAGO ----------
Bonder, J.F., Rossi, J.D. "Existence results for the p-Laplacian with nonlinear boundary conditions" . Journal of Mathematical Analysis and Applications 263, no. 1 (2001) : 195-223.
http://dx.doi.org/10.1006/jmaa.2001.7609
---------- MLA ----------
Bonder, J.F., Rossi, J.D. "Existence results for the p-Laplacian with nonlinear boundary conditions" . Journal of Mathematical Analysis and Applications, vol. 263, no. 1, 2001, pp. 195-223.
http://dx.doi.org/10.1006/jmaa.2001.7609
---------- VANCOUVER ----------
Bonder, J.F., Rossi, J.D. Existence results for the p-Laplacian with nonlinear boundary conditions. J. Math. Anal. Appl. 2001;263(1):195-223.
http://dx.doi.org/10.1006/jmaa.2001.7609