Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity
Abstract This paper is mainly concerned with the boundary value problems for the general Schrödinger equation with general superlinear nonlinearity introduced in (Sun et al. in J. Inequal. Appl. 2018:100, 2018). We firstly study a new algorithm for finding the meromorphic solution for the mentioned...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1212-2 |
| _version_ | 1818137457269407744 |
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| author | Hongjun He Zhifeng Pang |
| author_facet | Hongjun He Zhifeng Pang |
| author_sort | Hongjun He |
| collection | DOAJ |
| description | Abstract This paper is mainly concerned with the boundary value problems for the general Schrödinger equation with general superlinear nonlinearity introduced in (Sun et al. in J. Inequal. Appl. 2018:100, 2018). We firstly study a new algorithm for finding the meromorphic solution for the mentioned equation via meromorphic inequalities presented in (Xu in J. Math. Study 38(1):71–86, 2015). Then we deal with the necessary and sufficient conditions of convergence and obtain the general solutions and the conditions of solvability for the mentioned equation by means of the meromorphic inequalities for the classical boundary value problems developed in (Guillot in J. Nonlinear Math. Phys. 25(3):497–508, 2018). These results generalize some previous results concerning the asymptotic behavior of solutions of non-delay systems of Schrödinger equations by applying the maximum principle approach with respect to the Schrödinger operator in (Wan in J. Inequal. Appl. 2017:104, 2017). |
| first_indexed | 2024-12-11T09:56:36Z |
| format | Article |
| id | doaj.art-21c256082de34d3fa77bebb4ce09b33b |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-11T09:56:36Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-21c256082de34d3fa77bebb4ce09b33b2022-12-22T01:12:14ZengSpringerOpenBoundary Value Problems1687-27702019-05-012019111810.1186/s13661-019-1212-2Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearityHongjun He0Zhifeng Pang1Department of Basic Teaching, Zhengzhou University of Industrial TechnologySchool of Mathematics and Statistics, Henan UniversityAbstract This paper is mainly concerned with the boundary value problems for the general Schrödinger equation with general superlinear nonlinearity introduced in (Sun et al. in J. Inequal. Appl. 2018:100, 2018). We firstly study a new algorithm for finding the meromorphic solution for the mentioned equation via meromorphic inequalities presented in (Xu in J. Math. Study 38(1):71–86, 2015). Then we deal with the necessary and sufficient conditions of convergence and obtain the general solutions and the conditions of solvability for the mentioned equation by means of the meromorphic inequalities for the classical boundary value problems developed in (Guillot in J. Nonlinear Math. Phys. 25(3):497–508, 2018). These results generalize some previous results concerning the asymptotic behavior of solutions of non-delay systems of Schrödinger equations by applying the maximum principle approach with respect to the Schrödinger operator in (Wan in J. Inequal. Appl. 2017:104, 2017).http://link.springer.com/article/10.1186/s13661-019-1212-2Boundary value problemMaximum principle approachGeneral Schrödinger equation |
| spellingShingle | Hongjun He Zhifeng Pang Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity Boundary Value Problems Boundary value problem Maximum principle approach General Schrödinger equation |
| title | Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity |
| title_full | Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity |
| title_fullStr | Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity |
| title_full_unstemmed | Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity |
| title_short | Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity |
| title_sort | solvability for boundary value problem of the general schrodinger equation with general superlinear nonlinearity |
| topic | Boundary value problem Maximum principle approach General Schrödinger equation |
| url | http://link.springer.com/article/10.1186/s13661-019-1212-2 |
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