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Sobre el problema parabólico periódico L[u] = f(x,t,u,Du)
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Teorema de comparación, Dominio acotado, Caso elíptico, Teoría abstracta (es)Caso elíptico, Teoría abstracta (en)
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ABSTRACT. Sufficient conditions are obtained for the existence of solutions of the nonlinear periodic problem:
L[u] = f(x, t, u(x, t), ⊽ xu(x, t)) on Ω x ℝ
u(x, t + T) = u(x, t) on Ω x ℝ, u = 0 on 3 Ω x ℝ
where L is a second order uniformly parabolic differentital operator
Referencias
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AMANN, H. Y CRANDALL, M. G., On some existence theorems for semi-linear elliptic equations, Indiana University Mathematics Journal, Vol. 27, N° 5, (1978).
FRIEDMAN, A., Partial Differencial Equations, of Parabolic Type, Prentice Hall, Inc. Englewood, Cliffs, N. J., 1964.
FRIEDMAN, A., Partial Differencial Equations, Holt, Rinehart and Winston, Inc. New York, 1969.
KAZDAN, J. L. Y KRAMER, R. J., Invariant criteria for existence of solutions to second order quasilinear elliptic equations, Comm, Pure Appl. Math. XXXI (1978), 619-645.
KOLESOV, JU S., A test for the existence of periodic solutions to parabolic equations, Sovieth Math. Dokl. 7 (1966), 1318-1320.
LADYZENSAKAJA, O. A., SOLONNIKOV, V. A. AND URALCEVA, N. N., Linear and Quasi-Linear Equations of Parabolic Type, American Mathematical Society. Providence, Rhode Island, 1968, (Translated from the Russian).
LAZER, A. C., Some Remarks on Periodic Solutions of Parabolic Differential Equations, Dynamical Systems II, ed. Bednarek-Cesari, Academic Press, 1982, p. 227-246.
ORTEGA, L., Sobre las soluciones periódicas del problema de Dirichlet para ecuaciones de tipo parabólico, Rev. Colombiana de Matemáticas. Vol. XIX, (1985), 233-250.
POHOZAEV, S. I., On equations of the form Au = f(x, u Du). Math. USSR Sbomik. 41, (1982), N°2.
PROTTER, M. AND WEINBERGER, H., Maximum Principles in Differential Equations, Prentice Hall, Englewood, Cliffs, N. J., 1967.
SMULEV, I., Periodic solutions of the first boundary problem for parabolic equations, Trans. Amer. Math. Soc., 79 (216-229), (1969), UDC 517. 94.1.9.
