Cómo citar
Descargas
Artículos más leídos del mismo autor/a
- Jorge Cossio, Existencia y multiplicidad de soluciones para problemas elípticos semilineales y cuasilineales , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 39 Núm. 151 (2015)
- Jorge Cossio, Germán Jiménez, APLICACION DE UN PRINCIPIO DE MINIMIZACIÓN , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 28 Núm. 106 (2004)
Métricas Alternativas
Dimensions
Resumen
En este artículo se presentan los resultados más importantes de mi trabajo de investigación en el estudio de la existencia y de las propiedades de las soluciones de ecuaciones diferenciales parciales no lineales.
Donde λ ∈ R, Ω es un dominio acotado en RN con frontera suave, ∆ = n i=0 ∂/∂x2 i es el operador de Laplace y f : R → R es una función no lineal. Se presentan teoremas obtenidos utilizando teoría de bifurcación, métodos variacionales y un principio de minimax desarrollado por el autor en colaboración con A. Castro y J. M. Neuberger ([Cas-Cos-Nu1], 1997). Además, se incluyen algunos algoritmos para construir y visualizar soluciones a problemas no lineales del tipo (1) y una serie de preguntas abiertas.
Palabras clave
Citas
[Ad-Cas] H. Adu ́en and A. Castro, Infinitely Many Nonradial Solutions to a Superlinear Dirichlet Problem, Proc. Amer. Math. Soc. 131 (2003), 835–843.
[Am-Pro] A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis, Cambridge Studies in Advanced Mathematics 34, Cambridge University Press, Cambridge 1993.
[Am-Ra] A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory, J. Funct. Anal. 14 (1973), 349–381.
[Ar-Cos1] H. Arango y J. Cossio, Construcci ́on de Soluciones Radialmente Sim ́etricas para un Problema El ́ıptico Semilineal, Rev. Colombiana Mat.30 (1996), 77–92.
[Ar-Cos2] H. Arango and J. Cossio, Explicit Construction, Uniqueness, and Bifurcation curves of Solutions for a Nonlinear Dirichlet Problem in a Ball, Electronic Journal of Differential Equations, Conf. 05, 2000, 1–12.
[Cas1] A. Castro, M ́etodos de Reducci ́on via Minimax, Primer Simposio Colombiano de An ́alisis Funcional, Medell ́ın, Colombia, (1981).
[Cas-Cos1] A. Castro and J. Cossio, A Bifurcation Theorem and Applications, Dynamic Systems and Applications 2 (1993), 221–226.
[Cas-Cos2] A. Castro and J. Cossio, Multiple Radial Solutions for a Semilinear Dirichlet Problem in a ball, Rev. Colombiana Mat. 27 (1993), 15–24.
[Cas-Cos3] A. Castro and J. Cossio, Multiple Solutions for a Nonlinear Dirichlet Problem, SIAM J. Math. Anal. 25 (1994), 1554–1561.
[Cas-Cos-Nu1] A. Castro, J. Cossio and J. M. Neuberger, A Sign-Changing Solution for a Superlinear Dirichlet Problem, Rocky Mountain J.M. 27 (1997), 1041–1053.
[Cas-Cos-Nu2] A. Castro, J. Cossio and J. M. Neuberger, On Multiple Solutions of a Nonlinear Dirichlet Problem, Nonlinear Analysis, Theory, Methods & Applications, 30 (1997), 3657–3662.
[Cas-Cos-Nu3] A. Castro, J. Cossio and J. M. Neuberger, A Minimax Principle, Index of the Critical Point, and Existence of Sign-changing Solutions to Elliptic Boundary Value Problems, Electronic Journal of Differential Equations 1998 (1998), 1–18.
[Cas-Laz1] A. Castro and A. C. Lazer, Applications of a Max-min Principle, Rev. Colombiana Mat. 10 (1976), 141–149.
[Cas-Laz2] A. Castro and A. C. Lazer, Critical Point Theory and the Number of Solutions of a Nonlinear Dirichlet Problem, Ann. Mat. Pura Appl. 70 (1979), 113–137.
[Cos] J. Cossio, M ́ultiples Soluciones para un Problema El ́ıptico Semilineal. En Memorias de la III Escuela de Verano en geometr ́ıa diferencial, ecuaciones diferenciales parciales y an ́alisis num ́erico. Academia Colombiana de Ciencias Exactas F ́ısicas y Naturales, Colecci ́on memorias No. 7, 1995, 53–59.
[Cos-Le-Nu] J. Cossio, S. Lee, and J. M. Neuberger, A Reduction Algorithm for Sublinear Dirichlet Problems, Nonlinear Analysis, 47 (2001), 3379–3390.
[Cos-He] J. Cossio and S. Herr ́on, Nontrivial Solutions for a Semilinear Dirichlet Problem with Nonlinearity Crossing Multiples Eigenvalues, Submitted for publication in the Journal of Dynamics and Differential Equations.
[Cos-Ve] J. Cossio y C. V ́elez, Soluciones no Triviales para un Problema de Dirichlet Asint ́oticamente Lineal, Aceptado para publicaci ́on en la Revista Colombiana de Matem ́aticas, 2003.
[Ch] S. Chandrasekhar, An Introduction to the Study of Stellar Structure, University of Chicago Press, 1939.
[Cr-Ra] M. Crandall and P. Rabinowitz, Bifurcation from Simple Eigenvalue, J. Funct. Anal. 8 (1971), 321–340.
[Da] E. Dancer, Counterexamples to Some Conjectures on the Number of Solutions of Nonlinear Equations, Math. Ann. 16 (1976), 1361–1376.
[De-War] E. Deumens and H. Warchall, Explicit Construction of all Spherical Symmetric Solitary Waves for a Nonlinear Wave Equation in Multiple Dimensions, Nonlinear Analysis, Theory, Methods and Applications 12 (1988), 419–447.
[Ek] I. Ekeland, On the Variational Principle, J. Math. Anal. Appl. 47 (1974), 324–353.
[Es] M. Esteban, Multiple Solutions of Semilinear Elliptic Problems in a Ball, J. Differential Equations 57 (1985), 112–137.
[He] M. Henon, Numerical Experiments on the Stability of spherical Stellar Systems, Astro. Astrophys. 24 (1973), 229–238.
[Li-Ya] E. Lieb and H. T. Yau, The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics, Commun. Math. Phys. 112 (1987), 147–174.
[Ke-An] J. Keller and S. Antman, Bifurcation Theory and Nonlinear Eigenvalue problems, W. A. Benjamin, Inc., New York, 1969, 395-409.
[Lan-Laz-Me] E. M. Landesman, A. C. Lazer, and D. Meyers, On Saddle Point Problems in the Calculus of Variations, the Ritz Algorithm, and Monotone Convergence, J. Math. Anal. Appl. 53 (1975), 594–614.
[Laz-Sol] A. C. Lazer and S. Solimini, Nontrivial Solutions of Operator Equations and Morse Indices of Critical Points of Min-Max Type, Nonlinear Analysis TMA 12 (1988), 761–775.
[Lj-Sc] L. Ljusternik and L. Schnirelman, M ́ethodes Topologiques dans les Probl ́emes Variationnels, Hermann, Paris, 1934.
[Mors1] M. Morse, Relations Between the Critical Points of a Real Function of n Independent Variables, Trans. Amer. Math. Soc. 27 (1925), 345–396.
[Mors2] M. Morse, The Calculus of Variations in the Large, Amer. Math. Soc. Colloq. Publ., 18, 1934.
[Pa-Sm] R. Palais and S. Smale, A Generalized Morse Theory, Bull. Amer. Math. Soc. 70 (1964), 165–171.
[Ra1] P. Rabinowitz, Some Global Results for Nonlinear Eigenvalue Problems, J. Funct. Anal. 7 (1971), 487-513.
[Ra2] P. Rabinowitz, Topological Methods in Bifurcation Theory, S ́eminaire de Math ́ematiques Sup ́erieures, S ́eminaire Scientifique OTAN, Les Presses de l’Universit ́e de Montreal, Montreal, 1985.
[Ra3] P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential equations, Regional Conference Series in Mathematics, 65, Providence, R. I., AMS (1986).
[Wa] Z. Q. Wang, On a Superlinear Elliptic Equation, Ann. Inst. H. Poincar ́e. Analyse Non Lin ́eaire 8 (1991), 43–57.
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.
Derechos de autor 2023 https://creativecommons.org/licenses/by-nc-nd/4.0