Application of p-regularity theory to the Duffing equation
Abstract The paper studies a solution existence problem of the nonlinear Duffing equation of the form F ( x , μ , β ) = x ″ + x + μ x 3 − β sin t = 0 , β > 0 , μ ≠ 0 , $$ F(x,\mu, \beta)=x''+x+\mu x^{3}-\beta\sin t = 0,\quad \beta > 0, \mu\neq0, $$ where F : C 2 [ 0 , 2 π ] × R × R →...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-06-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-017-0815-8 |
| Summary: | Abstract The paper studies a solution existence problem of the nonlinear Duffing equation of the form F ( x , μ , β ) = x ″ + x + μ x 3 − β sin t = 0 , β > 0 , μ ≠ 0 , $$ F(x,\mu, \beta)=x''+x+\mu x^{3}-\beta\sin t = 0,\quad \beta > 0, \mu\neq0, $$ where F : C 2 [ 0 , 2 π ] × R × R → C [ 0 , 2 π ] $F: \mathcal{C}^{2}[0,2\pi]\times\mathbb{R}\times \mathbb{R}\rightarrow\mathcal{C}[0,2\pi]$ and x ( 0 ) = x ( 2 π ) = 0 $x(0)=x(2\pi)=0$ using the p-regularity theory. |
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| ISSN: | 1687-2770 |