Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
Soluciones no triviales para un problema de Dirichlet asintóticament lineal
Keywords:
Ecuación elíptica semilineal, Soluciones de cambio de señal (es)Semilinear elliptic equation, Sign-changing solutions, Leray-Scauder degree, 2000 Mathematics Subject Classification, . Primary: 35J20, Secondary: 35J25, 35J60 (en)
Downloads
Se demuestra que un problema elíptico semilineal tiene por lo menos tres soluciones no triviales cuando el rango de la derivada de la no linealidad incluye al menos los dos primeros valores propios. Dos de las soluciones son de un signo (positivo y negativo, respectivamente) y la tercera solución cambia de signo. En la demostración se usan, de manera esencial, el Teorema del Paso de la Montaña y la teoría de grado de Leray-Schauder.
Abstract. We prove that a semilinear elliptic boundary value problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Two of them are of one sign (positive and negative, respectively), and the third solution changes sign. Extensive use is made of the Mountain Pass Theorem and the Leray-Schauder degree
References
R. Adams, Sobolev Spaces, New York, Academic Press, 1975.
S. Agmon, The Lp approach to the Dirichlet problem, Ann. Scuola Norm. Sup. Pisa, 13, (1959), 405-448.
H. Amann, A Note on Degree Theory for Gradient Mappings, Proc. of the A.M.S., 85 no. 4 (1982), 591-595.
A. Ambrosetti & G. Mancini, Sharp nonuniqueness results for some nonlinear problems, Nonlinear Anal., 3 no. 5 (1979), 635-645.
A. Ambrosetti & P. Rabinowitz, Dual variational methods in critical point theory, J. Funct. Anal., 14 (1973), 343-381.
T. Bartsch & Z. Q. Wang, On the Existence of Sign Changing Solutions for Semilinear Dirichlet Problems, Topological Methods in Nonlinear Analysis, 7 (1996), 115-131.
A. Castro, Métodos de Reducción via Minimax, Primer Simposio Colombiano de Análisis Funcional, Medellín, Colombia, 1981.
A. Castro, Non Linear Functional Analysis, II Escuela de Verano en Geometría Diferencial, Análisis Numérico y Ecuaciones Diferenciales Parciales, Universidad Nacional, Medellín, Colombia, 1994.
A. Castro AND J. Cossio, Multiple Radial Solutions for a Semilinear Dirichlet Problem in a ball, Rev. Colombiana Math., 2 7 (1993), 15-24.
A. Castro & J. Cossio, Multiple Solutions for a Nonlinear Dirichlet Problem, SIAM J. Math. Anal., 2 5 (1994), 1554-1561.
A. Castro, J. Cossio & J. M. Neuberger, Sign-Changing Solutions for a Superlinear Dirichlet Problem, Rocky Mountain J. M., 2 7 no. 4 (1997), 1041-1053.
A. Castro, J. Cossio & J. M. Neuberger, On Multiple Solutions of a Nonlinear Dirichlet Problem, Nonlinear Analysis, Theory, Methods & Applications, 30 no. 6 (1997), 3657-3662.
A. Castro & A. Kurepa, Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball with Jumping Nonlinearities, Trans. Amer. Math. Soc. 315 no. 1 (1989), 353-372.
A. Castro & A. C. Lazer, Critical Point Theory and the Number of Solutions of a Nonlinear Dirichlet Problem, Ann. Mat. Pura Appl., 70 no. 4 (1979), 113—137.
K. C. Chang, Solutions of asymptotically linear operator equations via Morse Theory, Comm. Pure Appl. Math., 34 no. 5 (19 8 1), 693-712.
R. Courant & D. Hilbert, Methods of Mathematical Physics, Volume I, New York, John Wiley, 1989.
H. Hofer, The Topological Degree at a Critical Point of Mountain Pass Type, Proc. Sympos. Pure Math., 45 (1986), 501-509.
A. C. Lazer & J. P. McKenna, Multiplicity Results for a Class of Semilinear Elliptic and Parabolic Boundary Value Problems, J. Math. Anal. Appl., 107 (1985), 371-395.
P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Regional Conference Series in Mathematics, 65, Providence, R.I., A M S (1986).
M. Struwe, Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Berlin, New York, Springer-Verlag, 1990.
Z. Q. Wang, On a Superlinear Elliptic Equation, Ann. Inst. H. Poincare Analyse Non Lineaire 8 (1991) 43-57.
