Existence of multiple solutions for a class of second-order ordinary differential equations
By means of variational structure and $Z_2$ group index theory, we obtain multiple solutions for the second-order differential equation $$ frac{d}{dt}(p(t)frac{du}{dt})+q(t)u+f(t,u)=0 ,quad 0 less than t less than 1, $$ subject to one of the following two sets of boundary conditions: $$ u'(0...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2004-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/137/abstr.html |
| _version_ | 1817987222318612480 |
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| author | Xiao-Bao Shu Yuan-Tong Xu |
| author_facet | Xiao-Bao Shu Yuan-Tong Xu |
| author_sort | Xiao-Bao Shu |
| collection | DOAJ |
| description | By means of variational structure and $Z_2$ group index theory, we obtain multiple solutions for the second-order differential equation $$ frac{d}{dt}(p(t)frac{du}{dt})+q(t)u+f(t,u)=0 ,quad 0 less than t less than 1, $$ subject to one of the following two sets of boundary conditions: $$ u'(0) = u(1)+ u'(1)=0quadhbox{or}quad u(0)=u(1)=0,. $$ |
| first_indexed | 2024-04-14T00:19:13Z |
| format | Article |
| id | doaj.art-b4492e43b3954cc1912b5dc00bc70bc5 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-14T00:19:13Z |
| publishDate | 2004-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-b4492e43b3954cc1912b5dc00bc70bc52022-12-22T02:23:02ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-11-012004137114Existence of multiple solutions for a class of second-order ordinary differential equationsXiao-Bao ShuYuan-Tong XuBy means of variational structure and $Z_2$ group index theory, we obtain multiple solutions for the second-order differential equation $$ frac{d}{dt}(p(t)frac{du}{dt})+q(t)u+f(t,u)=0 ,quad 0 less than t less than 1, $$ subject to one of the following two sets of boundary conditions: $$ u'(0) = u(1)+ u'(1)=0quadhbox{or}quad u(0)=u(1)=0,. $$http://ejde.math.txstate.edu/Volumes/2004/137/abstr.htmlVariational structure$Z_2$ group index theorycritical pointsboundary value problems. |
| spellingShingle | Xiao-Bao Shu Yuan-Tong Xu Existence of multiple solutions for a class of second-order ordinary differential equations Electronic Journal of Differential Equations Variational structure $Z_2$ group index theory critical points boundary value problems. |
| title | Existence of multiple solutions for a class of second-order ordinary differential equations |
| title_full | Existence of multiple solutions for a class of second-order ordinary differential equations |
| title_fullStr | Existence of multiple solutions for a class of second-order ordinary differential equations |
| title_full_unstemmed | Existence of multiple solutions for a class of second-order ordinary differential equations |
| title_short | Existence of multiple solutions for a class of second-order ordinary differential equations |
| title_sort | existence of multiple solutions for a class of second order ordinary differential equations |
| topic | Variational structure $Z_2$ group index theory critical points boundary value problems. |
| url | http://ejde.math.txstate.edu/Volumes/2004/137/abstr.html |
| work_keys_str_mv | AT xiaobaoshu existenceofmultiplesolutionsforaclassofsecondorderordinarydifferentialequations AT yuantongxu existenceofmultiplesolutionsforaclassofsecondorderordinarydifferentialequations |