Some generic properties of nonlinear second order diffusional type problem

Vladimír Ďurikovič; Mária Ďurikovičová

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 3, page 229-244
  • ISSN: 0044-8753

Abstract

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We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.

How to cite

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Ďurikovič, Vladimír, and Ďurikovičová, Mária. "Some generic properties of nonlinear second order diffusional type problem." Archivum Mathematicum 035.3 (1999): 229-244. <http://eudml.org/doc/248374>.

@article{Ďurikovič1999,
abstract = {We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.},
author = {Ďurikovič, Vladimír, Ďurikovičová, Mária},
journal = {Archivum Mathematicum},
keywords = {Fredholm operator; Hölder space; bifurcation set; parabolic type operator; locally invertible operator; Fredholm operator; Hölder space; bifurcation set; parabolic type operator; locally invertible operator},
language = {eng},
number = {3},
pages = {229-244},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some generic properties of nonlinear second order diffusional type problem},
url = {http://eudml.org/doc/248374},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Ďurikovič, Vladimír
AU - Ďurikovičová, Mária
TI - Some generic properties of nonlinear second order diffusional type problem
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 3
SP - 229
EP - 244
AB - We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.
LA - eng
KW - Fredholm operator; Hölder space; bifurcation set; parabolic type operator; locally invertible operator; Fredholm operator; Hölder space; bifurcation set; parabolic type operator; locally invertible operator
UR - http://eudml.org/doc/248374
ER -

References

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  5. Generic properties of nonlinear boundary value problems, Differential Equations and Mathematical Physics (1992), Academic Press Inc., New York, 217-234. (1992) Zbl0756.47047MR1126697
  6. Fredholm mappings and the generalized boundary value problem, Differential and Integral Equation 8 Nr.1 (1995), 19-40. (1995) MR1296108
  7. “Mathematical analysis”, ALFA, vydavatelstvo technickej a ekonomickej literatury, Bratislava, 1974. (in Slovak) (1974) 
  8. Introduction of Functional Analysis, John Wiley and Sons, Inc., New York, 1958. (1958) MR0098966
  9. Functional Analysis, Nauka, Moscow, 1980. (in Russian) (1980) Zbl0517.46001MR0598629
  10. Functional Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1980. (1980) Zbl0435.46002MR0617913

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