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 |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/81/abstr.html |
| Summary: | 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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| ISSN: | 1072-6691 |