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1991 | 54 | 2 | 111-116
Tytuł artykułu

Periodic-Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study the periodic-Neumann boundary value problem for a class of nonlinear parabolic equations. We prove a new uniqueness result and study the structure of the set of solutions when there exist more than one solution. The ideas are applied to a Neumann problem for an elliptic equation.
Słowa kluczowe
Rocznik
Tom
54
Numer
2
Strony
111-116
Opis fizyczny
Daty
wydano
1991
otrzymano
1989-02-08
Twórcy
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela, Spain
Bibliografia
  • [1] S. Ahmad, A resonance problem in which the nonlinearity may grow linearly, Proc. Amer. Math. Soc. 92 (1984), 381-384.
  • [2] H. Amann, Periodic solutions of semilinear parabolic equations, in: Nonlinear Analysis, Academic Press, New York 1978, 1-29.
  • [3] D. W. Bange, Periodic solutions of a quasilinear parabolic differential equation, J. Differential Equations 17 (1975), 61-72.
  • [4] J. W. Bebernes and M. Martelli, On the structure of the solution set for periodic boundary value problems, Nonlinear Anal. 4 (1980), 821-830.
  • [5] J. W. Bebernes and K. Schmitt, Invariant sets and Hukuhara-Kneser property for systems of parabolic partial differential equations, Rocky Mountain J. Math. 7 (1977), 557-567.
  • [6] L. Cesari, Functional analysis, nonlinear differential equations and the alternative method, in: Nonlinear Functional Analysis and Differential Equations, Marcel Dekker, New York 1976, 1-197.
  • [7] L. Cesari and R. Kannan, An abstract theorem at resonance, Proc. Amer. Math. Soc. 63 (1977), 221-225.
  • [8] L. Cesari and R. Kannan, An existence theorem for periodic solutions of nonlinear parabolic equations, Istit. Lombardo Accad. Sci. Lett. Rend. A 116 (1985), 19-26.
  • [9] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
  • [10] R. Kannan and V. Lakshmikantham, Existence of periodic solutions of semilinear parabolic equations and the method of upper and lower solutions, J. Math. Anal. Appl. 97 (1983), 291-299.
  • [11] P. J. McKenna, Uniqueness of solutions for semilinear equations at resonance, Nonlinear Anal. 2 (1978), 235-237.
  • [12] J. Mawhin, Semi-coercive monotone variational problems, Acad. Roy. Belg. Bull. Cl. Sci. (5) 73 (1987), 118-130.
  • [13] J. J. Nieto, Periodic solutions of nonlinear parabolic equations, J. Differential Equations 60 (1985), 90-102.
  • [14] J. J. Nieto, Nonuniqueness of solutions for semilinear elliptic equations at resonance, Boll. Un. Mat. Ital. (6) 5-A (1986), 205-210.
  • [15] J. J. Nieto, Decreasing sequences of compact absolute retracts and nonlinear problems, Boll. Un. Mat. Ital. (7) 2-B (1988), 497-507.
  • [16] T. I. Seidman, Periodic solutions of a nonlinear parabolic equation, J. Differential Equations 19 (1975), 242-257.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv54z2p111bwm
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