Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations
By means of the shooting method together with the maximum principle and the Kneser–Hukahara continuum theorem, the authors present the existence, uniqueness and qualitative properties of solutions to nonlinear second-order boundary value problem on the semi-infinite interval of the following type: $...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2021-01-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8631 |
| _version_ | 1797830483712671744 |
|---|---|
| author | Minghe Pei Libo Wang Xuezhe Lv |
| author_facet | Minghe Pei Libo Wang Xuezhe Lv |
| author_sort | Minghe Pei |
| collection | DOAJ |
| description | By means of the shooting method together with the maximum principle and the Kneser–Hukahara continuum theorem, the authors present the existence, uniqueness and qualitative properties of solutions to nonlinear second-order boundary value problem on the semi-infinite interval of the following type:
$$
\begin{cases}
y''=f(x,y,y'),& x\in[0,\infty), \\
y'(0)=A,& y(\infty)=B
\end{cases}
$$
and
$$
\begin{cases}
y''=f(x,y,y'),& x\in[0,\infty), \\
y(0)=A,&y(\infty)=B,
\end{cases}
$$
where $A,B\in \mathbb{R}$, $f(x,y,z)$ is continuous on $[0,\infty)\times\mathbb{R}^2$. These results and the matching method are then applied to the search of solutions to the nonlinear second-order non-autonomous boundary value problem on the real line
$$
\begin{cases}
y''=f(x,y,y'), & x\in\mathbb{R} ,\\
y(-\infty)=A,& y(\infty)=B,
\end{cases}
$$
where $A\not=B$, $f(x,y,z)$ is continuous on $\mathbb{R}^3$. Moreover, some examples are given to illustrate the main results, in which a problem arising in the unsteady flow of power-law fluids is included. |
| first_indexed | 2024-04-09T13:36:50Z |
| format | Article |
| id | doaj.art-02d82bd5aadf43f595981eed10beb248 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:50Z |
| publishDate | 2021-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-02d82bd5aadf43f595981eed10beb2482023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-01-012021112110.14232/ejqtde.2021.1.18631Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equationsMinghe Pei0Libo Wang1Xuezhe Lv2Beihua University, Jilin City, P.R. ChinaBeihua University, Jilin City, P.R. ChinaBeihua University, Jilin City, P.R. ChinaBy means of the shooting method together with the maximum principle and the Kneser–Hukahara continuum theorem, the authors present the existence, uniqueness and qualitative properties of solutions to nonlinear second-order boundary value problem on the semi-infinite interval of the following type: $$ \begin{cases} y''=f(x,y,y'),& x\in[0,\infty), \\ y'(0)=A,& y(\infty)=B \end{cases} $$ and $$ \begin{cases} y''=f(x,y,y'),& x\in[0,\infty), \\ y(0)=A,&y(\infty)=B, \end{cases} $$ where $A,B\in \mathbb{R}$, $f(x,y,z)$ is continuous on $[0,\infty)\times\mathbb{R}^2$. These results and the matching method are then applied to the search of solutions to the nonlinear second-order non-autonomous boundary value problem on the real line $$ \begin{cases} y''=f(x,y,y'), & x\in\mathbb{R} ,\\ y(-\infty)=A,& y(\infty)=B, \end{cases} $$ where $A\not=B$, $f(x,y,z)$ is continuous on $\mathbb{R}^3$. Moreover, some examples are given to illustrate the main results, in which a problem arising in the unsteady flow of power-law fluids is included.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8631semi-infinite intervalheteroclinic solutionshooting methodmaximum principlekneser–hukahara continuum theoremmatching method |
| spellingShingle | Minghe Pei Libo Wang Xuezhe Lv Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations Electronic Journal of Qualitative Theory of Differential Equations semi-infinite interval heteroclinic solution shooting method maximum principle kneser–hukahara continuum theorem matching method |
| title | Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations |
| title_full | Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations |
| title_fullStr | Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations |
| title_full_unstemmed | Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations |
| title_short | Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations |
| title_sort | existence uniqueness and qualitative properties of heteroclinic solutions to nonlinear second order ordinary differential equations |
| topic | semi-infinite interval heteroclinic solution shooting method maximum principle kneser–hukahara continuum theorem matching method |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8631 |
| work_keys_str_mv | AT minghepei existenceuniquenessandqualitativepropertiesofheteroclinicsolutionstononlinearsecondorderordinarydifferentialequations AT libowang existenceuniquenessandqualitativepropertiesofheteroclinicsolutionstononlinearsecondorderordinarydifferentialequations AT xuezhelv existenceuniquenessandqualitativepropertiesofheteroclinicsolutionstononlinearsecondorderordinarydifferentialequations |