Artículo
García-Melián, J.; Rossi, J.D.; De Lis, J.C.S. "A bifurcation problem governed by the boundary condition II" (2007) Proceedings of the London Mathematical Society. 94(1):1-25
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Abstract:
In this work we consider the problem Δ u = a(x)up in Ω, ∂u/∂v = λu on Ω Ω, where Ω is a smooth bounded domain, v is the outward unit normal to ∂Ω, λ is regarded as a parameter and 0 < p < 1. We consider both cases where a(x) > 0 in Ω or a(x) is allowed to vanish in a whole subdomain Ω0 of Ω. Our main results include existence of non-negative non-trivial solutions in the range 0 < λ < σ1, where σ1 is characterized by means of an eigenvalue problem, uniqueness and bifurcation from infinity of such solutions for small λ, and the appearance of dead cores for large enough λ. © 2006 London Mathematical Society.
Registro:
| Documento: | Artículo |
| Título: | A bifurcation problem governed by the boundary condition II |
| Autor: | García-Melián, J.; Rossi, J.D.; De Lis, J.C.S. |
| Filiación: | Departamento de Análisis Matemático, Universidad de La Laguna, C/ Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Instituto de Matemáticas y Física Fundamental, CSIC, C/ Serrano 123, 28006 Madrid, Spain |
| Año: | 2007 |
| Volumen: | 94 |
| Número: | 1 |
| Página de inicio: | 1 |
| Página de fin: | 25 |
| DOI: | http://dx.doi.org/10.1112/plms/pdl001 |
| Título revista: | Proceedings of the London Mathematical Society |
| Título revista abreviado: | Proc. Lond. Math. Soc. |
| ISSN: | 00246115 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246115_v94_n1_p1_GarciaMelian |
Referencias:
- Agmon, S., Douglis, A., Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I (1959) Comm. Pure Appl. Math., 12, pp. 623-727
- Amann, H., On the existence of positive solutions of nonlinear elliptic boundary value problems (1971) Indiana Univ. Math. J., 21, pp. 125-146
- Bandle, C., Sperb, R.P., Stakgold, I., Diffusion and reaction with monotone kinetics (1984) Nonlinear Anal. TMA, 8, pp. 321-333
- Beirão, H., Veiga, D.A., On the W2,p-regularity for solutions of mixed problems (1974) J. Math. Pures Appl., 53, pp. 279-290
- Deimling, K., (1985) Nonlinear Functional Analysis, , (Springer, Berlin)
- Del Pino, M., Positive solutions of a semilinear elliptic equation on a compact manifold (1994) Nonlinear Anal. TMA, 22, pp. 1423-1430
- Du, Y., Huang, Q., Blow-up solutions for a class of semilinear elliptic and parabolic equations (1999) SIAM J. Math. Anal., 31, pp. 1-18
- Fraile, J.M., Koch-Medina, P., López-GóMez, J., Merino, S., Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation (1996) J. Differential Equations, 127, pp. 295-319
- Friedman, A., Phillips, D., The free boundary of a semilinear elliptic equation (1984) Trans. Amer. Math. Soc., 282, pp. 153-182
- Garcia-Melian, J., Gomez-Renasco, R., Lopez-Gomez, J., Sabina De Lis, J.C., Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs (1998) Archive for Rational Mechanics and Analysis, 145 (3), pp. 261-289
- García-MeliáN, J., Rossi, J.D., Sabina De Lis, J., A bifurcation problem governed by the boundary condition I NoDEA Nonlinear Differential Equations Appl., , to appear
- García-MeliáN, J., Sabina De Lis, J., Uniqueness to quasilinear problems for the p-laplacian in radially symmetric domains (2001) Nonlinear Anal. TMA, 43, pp. 803-835
- Gidas, B., Spruck, J., A priori bounds for positive solutions of nonlinear elliptic equations (1981) Comm. Partial Differential Equations, 6, pp. 883-901
- Gilbarg, D., Trudinger, N.S., (1983) Elliptic Partial Differential Equations of Second Order, , (Springer, Berlin)
- Lieberman, G., Mixed boundary value problems for elliptic and parabolic differential equations of second order (1986) J. Math. Anal. Appl., 113, pp. 422-440
- Lieberman, G., Optimal holder regularity for mixed boundary value problems (1989) J. Math. Anal. Appl., 143, pp. 572-586
- López-GóMez, J., Sabina De Lis, J., First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs (1998) J. Differential Equations, 148, pp. 47-64
- Ouyang, T., On the positive solutions of semilinear equations Δ u + λu - Hup = 0 on the compact manifolds (1992) Trans. Amer. Math. Soc., 331, pp. 503-527
- Shamir, E., Regularization of mixed second-order elliptic problems (1968) Israel J. Math., 6, pp. 150-168
- Struwe, M., (1989) Variational Methods, , (Springer, New York)
Citas:
---------- APA ----------
García-Melián, J., Rossi, J.D. & De Lis, J.C.S. (2007) . A bifurcation problem governed by the boundary condition II. Proceedings of the London Mathematical Society, 94(1), 1-25.http://dx.doi.org/10.1112/plms/pdl001
---------- CHICAGO ----------
García-Melián, J., Rossi, J.D., De Lis, J.C.S. "A bifurcation problem governed by the boundary condition II" . Proceedings of the London Mathematical Society 94, no. 1 (2007) : 1-25.http://dx.doi.org/10.1112/plms/pdl001
---------- MLA ----------
García-Melián, J., Rossi, J.D., De Lis, J.C.S. "A bifurcation problem governed by the boundary condition II" . Proceedings of the London Mathematical Society, vol. 94, no. 1, 2007, pp. 1-25.http://dx.doi.org/10.1112/plms/pdl001
---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D., De Lis, J.C.S. A bifurcation problem governed by the boundary condition II. Proc. Lond. Math. Soc. 2007;94(1):1-25.http://dx.doi.org/10.1112/plms/pdl001
