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Abstract:

We study the existence of solutions an H-system for a revolution surface without boundary for H depending on the radius f. Under suitable conditions we prove that the existence of a solution is equivalent to the solvability of a scalar equation N(a) = L/√2, where N:script A⊂ℝ+→ℝ is a function depending on H. Moreover, using the method of upper and lower solutions we prove existence results for some particular examples. In particular, applying a diagonal argument we prove the existence of unbounded surfaces with prescribed H. Copyright © 2006 P. Amster et al.

Registro:

Documento: Artículo
Título:An H-system for a revolution surface without boundary
Autor:Amster, P.; De Nápoli, P.; Mariani, M.C.
Filiación:FCEyN, Departamento de Matemática, Pabellón I, (1428) Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas Y Técnicas (CONICET), Argentina
Department of Mathematical Sciences, New Mexico State University Las Cruces, NM 88003-8001, United States
Año:2006
Volumen:2006
DOI: http://dx.doi.org/10.1155/AAA/2006/93163
Título revista:Abstract and Applied Analysis
Título revista abreviado:Abstr. Appl. Anal.
ISSN:10853375
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_10853375_v2006_n_p_Amster.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10853375_v2006_n_p_Amster

Referencias:

  • Amster, P., Cassinelli, M.M., Mariani, M.C., Solutions to general quasilinear elliptic second order problems (2000) Nonlinear Studies, 7 (2), pp. 283-289. , Nonlinear Studies
  • Amster, P., Cassinelli, M.M., Mariani, M.C., Solutions to quasilinear equations by an iterative method (2000) Bulletin of the Belgian Mathematical Society. Simon Stevin, 7 (3), pp. 435-441. , Bulletin of the Belgian Mathematical Society. Simon Stevin
  • Amster, P., Mariani, M.C., Two iterative schemes for an H-system (2005) JIPAM. Journal of Inequalities in Pure and Applied Mathematics, 6 (17). , JIPAM. Journal of Inequalities in Pure and Applied Mathematics Article 5
  • Amster, P., Mariani, M.C., Rial, D.F., Existence and uniqueness of H-system's solutions with Dirichlet conditions (2000) Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 42 (4), pp. 673-677. , Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods
  • Brezis, H., Coron, J.-M., Multiple solutions of H-systems and Rellich's conjecture (1984) Communications on Pure and Applied Mathematics, 37 (2), pp. 149-187. , Communications on Pure and Applied Mathematics
  • Capietto, A., Mawhin, J., Zanolin, F., Boundary value problems for forced superlinear second order ordinary differential equations (1994) Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Vol. 12 (Paris, 1991-1993), 302, pp. 55-64. , Pitman Res. Notes Math. Ser. Longman Sci. Tech. Harlow
  • Gilbarg, D., Trudinger, N.S., (1983) Elliptic Partial Differential Equations of Second Order, 224, pp. xiii+513. , Grundlehren der mathematischen Wissenschaften Springer Berlin 2nd
  • Hildebrandt, S., On the Plateau problem for surfaces of constant mean curvature (1970) Communications on Pure and Applied Mathematics, 23, pp. 97-114. , Communications on Pure and Applied Mathematics
  • Struwe, M., (1988) Plateau's Problem and the Calculus of Variations, 35, pp. x+148. , Mathematical Notes Princeton University Press New Jersey
  • Wang, G.F., The Dirichlet problem for the equation of prescribed mean curvature (1992) Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, 9 (6), pp. 643-655. , Annales de l'Institut Henri Poincaré. Analyse Non Linéaire

Citas:

---------- APA ----------
Amster, P., De Nápoli, P. & Mariani, M.C. (2006) . An H-system for a revolution surface without boundary. Abstract and Applied Analysis, 2006.
http://dx.doi.org/10.1155/AAA/2006/93163
---------- CHICAGO ----------
Amster, P., De Nápoli, P., Mariani, M.C. "An H-system for a revolution surface without boundary" . Abstract and Applied Analysis 2006 (2006).
http://dx.doi.org/10.1155/AAA/2006/93163
---------- MLA ----------
Amster, P., De Nápoli, P., Mariani, M.C. "An H-system for a revolution surface without boundary" . Abstract and Applied Analysis, vol. 2006, 2006.
http://dx.doi.org/10.1155/AAA/2006/93163
---------- VANCOUVER ----------
Amster, P., De Nápoli, P., Mariani, M.C. An H-system for a revolution surface without boundary. Abstr. Appl. Anal. 2006;2006.
http://dx.doi.org/10.1155/AAA/2006/93163