On the generalized boundary value problem

Boris Rudolf

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 2, page 125-137
  • ISSN: 0044-8753

Abstract

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In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.

How to cite

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Rudolf, Boris. "On the generalized boundary value problem." Archivum Mathematicum 036.2 (2000): 125-137. <http://eudml.org/doc/248553>.

@article{Rudolf2000,
abstract = {In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.},
author = {Rudolf, Boris},
journal = {Archivum Mathematicum},
keywords = {Fredholm mapping; generalized BVP; dual problem; bounded nonlinearity; Landesman-Lazer conditions; Fredholm mapping; generalized boundary value problem; dual problem; bounded nonlinearity; Landesman-Lazer conditions},
language = {eng},
number = {2},
pages = {125-137},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the generalized boundary value problem},
url = {http://eudml.org/doc/248553},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Rudolf, Boris
TI - On the generalized boundary value problem
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 2
SP - 125
EP - 137
AB - In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.
LA - eng
KW - Fredholm mapping; generalized BVP; dual problem; bounded nonlinearity; Landesman-Lazer conditions; Fredholm mapping; generalized boundary value problem; dual problem; bounded nonlinearity; Landesman-Lazer conditions
UR - http://eudml.org/doc/248553
ER -

References

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  8. The generalized boundary value problem is a Fredholm mapping of index zero, Archivum Mathematicum 31 (1995), 55–58. (1995) Zbl0830.34013MR1342375
  9. Fredholm mappings and the generalized boundary value problem, Differential and Integral Equations 8 (1995), 19–40. (1995) MR1296108
  10. Generalized boundary value problems and Fredholm mappings, Nonlinear Analysis TMA 30 (1997), 1607–1616. (1997) MR1490083
  11. Generalized boundary value problems with linear growth, Mathematica Bohemica 123 (1998), 385–404. (1998) MR1667111
  12. Functional Analysis, Nauka, Moscow, 1980. (Russian) (1980) Zbl0517.46001MR0598629
  13. Applied Functional Analysis, Springer-Verlag, New York Berlin Heidelberg, 1995. (1995) Zbl0834.46002MR1347692

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