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

Juan J. Nieto

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 2, page 111-116
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Juan J. Nieto. "Periodic-Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation." Annales Polonici Mathematici 54.2 (1991): 111-116. <http://eudml.org/doc/262459>.

@article{JuanJ1991,
abstract = {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.},
author = {Juan J. Nieto},
journal = {Annales Polonici Mathematici},
keywords = {periodic Neumann boundary value problem; uniqueness; set of solutions},
language = {eng},
number = {2},
pages = {111-116},
title = {Periodic-Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation},
url = {http://eudml.org/doc/262459},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Juan J. Nieto
TI - Periodic-Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 2
SP - 111
EP - 116
AB - 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.
LA - eng
KW - periodic Neumann boundary value problem; uniqueness; set of solutions
UR - http://eudml.org/doc/262459
ER -

References

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  4. [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. Zbl0453.34019
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  8. [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. Zbl0593.35008
  9. [9] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964. Zbl0144.34903
  10. [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. Zbl0542.35044
  11. [11] P. J. McKenna, Uniqueness of solutions for semilinear equations at resonance, Nonlinear Anal. 2 (1978), 235-237. Zbl0383.35026
  12. [12] J. Mawhin, Semi-coercive monotone variational problems, Acad. Roy. Belg. Bull. Cl. Sci. (5) 73 (1987), 118-130. Zbl0647.49007
  13. [13] J. J. Nieto, Periodic solutions of nonlinear parabolic equations, J. Differential Equations 60 (1985), 90-102. Zbl0537.35049
  14. [14] J. J. Nieto, Nonuniqueness of solutions for semilinear elliptic equations at resonance, Boll. Un. Mat. Ital. (6) 5-A (1986), 205-210. Zbl0615.35037
  15. [15] J. J. Nieto, Decreasing sequences of compact absolute retracts and nonlinear problems, Boll. Un. Mat. Ital. (7) 2-B (1988), 497-507. Zbl0667.47035
  16. [16] T. I. Seidman, Periodic solutions of a nonlinear parabolic equation, J. Differential Equations 19 (1975), 242-257. Zbl0281.35005

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