Second order ODE; Dirichlet problem; variational method; critical point
In this note, we prove the existence of a solution to the semilinear second order ordinary differential equation $$displaylines{ u''(x)+ r(x) u'+g(x,u)=f(x),,cr x(0)=x(pi)=0,, }$$ using a variational method and critical point theory.
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| Format: | Article |
| Language: | English |
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Texas State University
2007-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/81/abstr.html |
| _version_ | 1811219347987759104 |
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| author | Petr Tomiczek |
| author_facet | Petr Tomiczek |
| author_sort | Petr Tomiczek |
| collection | DOAJ |
| description | In this note, we prove the existence of a solution to the semilinear second order ordinary differential equation $$displaylines{ u''(x)+ r(x) u'+g(x,u)=f(x),,cr x(0)=x(pi)=0,, }$$ using a variational method and critical point theory. |
| first_indexed | 2024-04-12T07:24:48Z |
| format | Article |
| id | doaj.art-3ee0e5d5b6e34b0baf7d077a5ef636fa |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T07:24:48Z |
| publishDate | 2007-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3ee0e5d5b6e34b0baf7d077a5ef636fa2022-12-22T03:42:13ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-05-0120078113Second order ODE; Dirichlet problem; variational method; critical pointPetr TomiczekIn this note, we prove the existence of a solution to the semilinear second order ordinary differential equation $$displaylines{ u''(x)+ r(x) u'+g(x,u)=f(x),,cr x(0)=x(pi)=0,, }$$ using a variational method and critical point theory.http://ejde.math.txstate.edu/Volumes/2007/81/abstr.htmlSecond order ODEDirichlet problemvariational methodcritical point |
| spellingShingle | Petr Tomiczek Second order ODE; Dirichlet problem; variational method; critical point Electronic Journal of Differential Equations Second order ODE Dirichlet problem variational method critical point |
| title | Second order ODE; Dirichlet problem; variational method; critical point |
| title_full | Second order ODE; Dirichlet problem; variational method; critical point |
| title_fullStr | Second order ODE; Dirichlet problem; variational method; critical point |
| title_full_unstemmed | Second order ODE; Dirichlet problem; variational method; critical point |
| title_short | Second order ODE; Dirichlet problem; variational method; critical point |
| title_sort | second order ode dirichlet problem variational method critical point |
| topic | Second order ODE Dirichlet problem variational method critical point |
| url | http://ejde.math.txstate.edu/Volumes/2007/81/abstr.html |
| work_keys_str_mv | AT petrtomiczek secondorderodedirichletproblemvariationalmethodcriticalpoint |