Construction of non-constant lower and upper functions for impulsive periodic problems
We present conditions ensuring the existence of piecewise linear lower and upper functions for the nonlinear impulsive periodic boundary value problem $u''=f(t,u,u'),$ $u(t_i+)=\mathrm{J}_i(u(t_i)),$ $u'(t_i+)=\mathrm{M}_i(u'(t_i)),$ $i=1,2,\dots,m,$ $u(0)=u(T),\,\,u'(0...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2004-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=206 |
| _version_ | 1797830782325096448 |
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| author | Irena Rachůnková Milan Tvrdy |
| author_facet | Irena Rachůnková Milan Tvrdy |
| author_sort | Irena Rachůnková |
| collection | DOAJ |
| description | We present conditions ensuring the existence of piecewise linear lower and upper functions for the nonlinear impulsive periodic boundary value problem
$u''=f(t,u,u'),$ $u(t_i+)=\mathrm{J}_i(u(t_i)),$ $u'(t_i+)=\mathrm{M}_i(u'(t_i)),$ $i=1,2,\dots,m,$ $u(0)=u(T),\,\,u'(0)=u'(T).$
This together with the existence principles which we proved in [5]-[7] allows us to prove new existence criteria, see Theorems 3.1 and 3.2. |
| first_indexed | 2024-04-09T13:41:38Z |
| format | Article |
| id | doaj.art-6e7d7a5213a649a2b303c653d38f1f0b |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:38Z |
| publishDate | 2004-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-6e7d7a5213a649a2b303c653d38f1f0b2023-05-09T07:52:57ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752004-08-012003191810.14232/ejqtde.2003.6.19206Construction of non-constant lower and upper functions for impulsive periodic problemsIrena Rachůnková0Milan Tvrdy1Palacky University, Olomouc, Czech RepublicMathematical Institute, Academy of Sciences of the Czech Republic, Prague, Czech RepublicWe present conditions ensuring the existence of piecewise linear lower and upper functions for the nonlinear impulsive periodic boundary value problem $u''=f(t,u,u'),$ $u(t_i+)=\mathrm{J}_i(u(t_i)),$ $u'(t_i+)=\mathrm{M}_i(u'(t_i)),$ $i=1,2,\dots,m,$ $u(0)=u(T),\,\,u'(0)=u'(T).$ This together with the existence principles which we proved in [5]-[7] allows us to prove new existence criteria, see Theorems 3.1 and 3.2.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=206 |
| spellingShingle | Irena Rachůnková Milan Tvrdy Construction of non-constant lower and upper functions for impulsive periodic problems Electronic Journal of Qualitative Theory of Differential Equations |
| title | Construction of non-constant lower and upper functions for impulsive periodic problems |
| title_full | Construction of non-constant lower and upper functions for impulsive periodic problems |
| title_fullStr | Construction of non-constant lower and upper functions for impulsive periodic problems |
| title_full_unstemmed | Construction of non-constant lower and upper functions for impulsive periodic problems |
| title_short | Construction of non-constant lower and upper functions for impulsive periodic problems |
| title_sort | construction of non constant lower and upper functions for impulsive periodic problems |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=206 |
| work_keys_str_mv | AT irenarachunkova constructionofnonconstantlowerandupperfunctionsforimpulsiveperiodicproblems AT milantvrdy constructionofnonconstantlowerandupperfunctionsforimpulsiveperiodicproblems |