Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space

Xian Xu; Bingjin Wang

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 4, page 399-409
  • ISSN: 0862-7959

Abstract

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In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.

How to cite

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Xu, Xian, and Wang, Bingjin. "Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space." Mathematica Bohemica 134.4 (2009): 399-409. <http://eudml.org/doc/38102>.

@article{Xu2009,
abstract = {In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.},
author = {Xu, Xian, Wang, Bingjin},
journal = {Mathematica Bohemica},
keywords = {sign-changing solution; operator equation in ordered Banach space; fixed point index; sign-changing solution; operator equation in ordered Banach space; fixed point index},
language = {eng},
number = {4},
pages = {399-409},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space},
url = {http://eudml.org/doc/38102},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Xu, Xian
AU - Wang, Bingjin
TI - Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 4
SP - 399
EP - 409
AB - In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.
LA - eng
KW - sign-changing solution; operator equation in ordered Banach space; fixed point index; sign-changing solution; operator equation in ordered Banach space; fixed point index
UR - http://eudml.org/doc/38102
ER -

References

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  9. Zhaoli Liu, Localized Critical Points in Banach Spaces and Sign Changing Solutions of Nonlinear p -Laplacian Equations, Topological Methods, Variational Methods. World Scientific Press, New Jersey (2002). (2002) MR2011692
  10. Xian Xu, Multiple sign-changing solutions for some m -point boundary value problems, Electron. J. Differ. Equ. (2004), 89 1-14. (2004) Zbl1058.34013MR2075428
  11. Xian Xu, Donal O'Regan, 10.1016/j.na.2007.05.030, Nonlinear Analysis 69 (2008), 434-447. (2008) MR2426260DOI10.1016/j.na.2007.05.030
  12. Xian Xu, Jingxian Sun, 10.1016/j.na.2004.07.023, Nonlinear Analysis 59 (2004), 491-505. (2004) MR2094426DOI10.1016/j.na.2004.07.023
  13. Xian Xu, Jingxian Sun, Donal O'Regan, 10.1016/j.na.2007.02.043, Nonlinear Analysis, 68 (2008), 3034-3046. (2008) MR2404815DOI10.1016/j.na.2007.02.043
  14. Kemei Zhang, Jingxian Sun, Multiple solutions for superlinear operator equations in Banach spaces and applications, Acta Math. Sinica (Chin. Ser.) 48 (2005), 99-108. (2005) MR2128657

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