Non-homogeneous BVPs for second-order symmetric Hamiltonian systems
By making use of Bolle’s method, we show that the following problem has infinitely many solutions: x¨+V′(x)=0,x(0)cosα−x˙(0)sinα=x0,x(1)cosβ−x˙(1)sinβ=x1,\begin{array}{rcl}\ddot{x}+{V}^{^{\prime} }\left(x)& =& 0,\\ x\left(0)\cos \alpha -\dot{x}\left(0)\sin \alpha & =& {x}_{0},\\ x\le...
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De Gruyter
2024-12-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0112 |
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| author | Chen Yingying Dong Yujun Wang Baiqian |
| author_facet | Chen Yingying Dong Yujun Wang Baiqian |
| author_sort | Chen Yingying |
| collection | DOAJ |
| description | By making use of Bolle’s method, we show that the following problem has infinitely many solutions: x¨+V′(x)=0,x(0)cosα−x˙(0)sinα=x0,x(1)cosβ−x˙(1)sinβ=x1,\begin{array}{rcl}\ddot{x}+{V}^{^{\prime} }\left(x)& =& 0,\\ x\left(0)\cos \alpha -\dot{x}\left(0)\sin \alpha & =& {x}_{0},\\ x\left(1)\cos \beta -\dot{x}\left(1)\sin \beta & =& {x}_{1},\end{array} where α,β∈(0,π)x0,x1∈Rn\alpha ,\beta \in \left(0,\pi ){x}_{0},{x}_{1}\in {{\rm{R}}}^{n} are given and V∈C2(Rn,R)V\in {C}^{2}\left({{\rm{R}}}^{n},{\rm{R}}) is even and is super-quadratic at infinity. |
| format | Article |
| id | doaj-art-eb13dd9e11734b39a65fe48cfe881ea6 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
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| series | Open Mathematics |
| spelling | doaj-art-eb13dd9e11734b39a65fe48cfe881ea62025-02-02T15:46:01ZengDe GruyterOpen Mathematics2391-54552024-12-0122122924310.1515/math-2024-0112Non-homogeneous BVPs for second-order symmetric Hamiltonian systemsChen Yingying0Dong Yujun1Wang Baiqian2School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, P. R. ChinaDepartment of Mathematics, Nanjing Normal University, Nanjing, 210097, Jiangsu, P. R. ChinaDongguan No. 6 Senior High School, 523400, Dongguan, P. R. ChinaBy making use of Bolle’s method, we show that the following problem has infinitely many solutions: x¨+V′(x)=0,x(0)cosα−x˙(0)sinα=x0,x(1)cosβ−x˙(1)sinβ=x1,\begin{array}{rcl}\ddot{x}+{V}^{^{\prime} }\left(x)& =& 0,\\ x\left(0)\cos \alpha -\dot{x}\left(0)\sin \alpha & =& {x}_{0},\\ x\left(1)\cos \beta -\dot{x}\left(1)\sin \beta & =& {x}_{1},\end{array} where α,β∈(0,π)x0,x1∈Rn\alpha ,\beta \in \left(0,\pi ){x}_{0},{x}_{1}\in {{\rm{R}}}^{n} are given and V∈C2(Rn,R)V\in {C}^{2}\left({{\rm{R}}}^{n},{\rm{R}}) is even and is super-quadratic at infinity.https://doi.org/10.1515/math-2024-0112sturm-liouvillehamiltonian systemnon-symmetric34b1534b2434l11 |
| spellingShingle | Chen Yingying Dong Yujun Wang Baiqian Non-homogeneous BVPs for second-order symmetric Hamiltonian systems Open Mathematics sturm-liouville hamiltonian system non-symmetric 34b15 34b24 34l11 |
| title | Non-homogeneous BVPs for second-order symmetric Hamiltonian systems |
| title_full | Non-homogeneous BVPs for second-order symmetric Hamiltonian systems |
| title_fullStr | Non-homogeneous BVPs for second-order symmetric Hamiltonian systems |
| title_full_unstemmed | Non-homogeneous BVPs for second-order symmetric Hamiltonian systems |
| title_short | Non-homogeneous BVPs for second-order symmetric Hamiltonian systems |
| title_sort | non homogeneous bvps for second order symmetric hamiltonian systems |
| topic | sturm-liouville hamiltonian system non-symmetric 34b15 34b24 34l11 |
| url | https://doi.org/10.1515/math-2024-0112 |
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