Computation of topological degree in ordered Banach spaces with lattice structure and applications

Yujun Cui

Applications of Mathematics (2013)

  • Volume: 58, Issue: 6, page 689-702
  • ISSN: 0862-7940

Abstract

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Using the cone theory and the lattice structure, we establish some methods of computation of the topological degree for the nonlinear operators which are not assumed to be cone mappings. As applications, existence results of nontrivial solutions for singular Sturm-Liouville problems are given. The nonlinearity in the equations can take negative values and may be unbounded from below.

How to cite

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Cui, Yujun. "Computation of topological degree in ordered Banach spaces with lattice structure and applications." Applications of Mathematics 58.6 (2013): 689-702. <http://eudml.org/doc/260648>.

@article{Cui2013,
abstract = {Using the cone theory and the lattice structure, we establish some methods of computation of the topological degree for the nonlinear operators which are not assumed to be cone mappings. As applications, existence results of nontrivial solutions for singular Sturm-Liouville problems are given. The nonlinearity in the equations can take negative values and may be unbounded from below.},
author = {Cui, Yujun},
journal = {Applications of Mathematics},
keywords = {cone; lattice; topological degree; cone; lattice; topological degree},
language = {eng},
number = {6},
pages = {689-702},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Computation of topological degree in ordered Banach spaces with lattice structure and applications},
url = {http://eudml.org/doc/260648},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Cui, Yujun
TI - Computation of topological degree in ordered Banach spaces with lattice structure and applications
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 6
SP - 689
EP - 702
AB - Using the cone theory and the lattice structure, we establish some methods of computation of the topological degree for the nonlinear operators which are not assumed to be cone mappings. As applications, existence results of nontrivial solutions for singular Sturm-Liouville problems are given. The nonlinearity in the equations can take negative values and may be unbounded from below.
LA - eng
KW - cone; lattice; topological degree; cone; lattice; topological degree
UR - http://eudml.org/doc/260648
ER -

References

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  8. Sun, J., Liu, X., 10.1006/jmaa.1996.0347, J. Math. Anal. Appl. 202 (1996), 785-796. (1996) Zbl0866.47043MR1408354DOI10.1006/jmaa.1996.0347
  9. Sun, J., Liu, X., Computation of topological degree for nonlinear operators and applications, Nonlinear Anal., Theory Methods Appl. 69 (2008), 4121-4130. (2008) Zbl1169.47043MR2463359
  10. Sun, J., Liu, X., 10.1016/j.jmaa.2008.05.023, J. Math. Anal. Appl. 348 (2008), 927-937. (2008) Zbl1177.47065MR2446045DOI10.1016/j.jmaa.2008.05.023
  11. Sun, J., Zhang, G., 10.1016/j.jmaa.2006.03.003, J. Math. Anal. Appl. 326 (2007), 242-251. (2007) Zbl1111.34023MR2277779DOI10.1016/j.jmaa.2006.03.003
  12. Walter, W., Ordinary Differential Equations. Transl. from the German by Russell Thompson. Graduate Texts in Mathematics. Readings in Mathematics 182, Springer New York (1998). (1998) MR1629775

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