Integral boundary value problems for second-order causal differential equations
Abstract This paper is concerned with second-order causal differential equations with Riemann–Stieltjes integral boundary conditions. To obtain sufficient conditions for the existence of extremal solutions for such problems, a novel comparison principle is first formulated. Next, the existence and u...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-03-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02030-w |
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| _version_ | 1849390333125722112 |
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| author | Wenli Wang Junyan Bao |
| author_facet | Wenli Wang Junyan Bao |
| author_sort | Wenli Wang |
| collection | DOAJ |
| description | Abstract This paper is concerned with second-order causal differential equations with Riemann–Stieltjes integral boundary conditions. To obtain sufficient conditions for the existence of extremal solutions for such problems, a novel comparison principle is first formulated. Next, the existence and uniqueness of the solutions for the second-order linear differential equations are proved based on the fixed point theorem. Then, the monotone iterative technique is employed to investigate the existence of the extremal solution, with the relative results being derived on the basis of upper and lower solutions. Finally, an example is provided to verify the theoretical results. |
| format | Article |
| id | doaj-art-c2760318de944d5cb061608366e5d21d |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-c2760318de944d5cb061608366e5d21d2025-08-20T03:41:42ZengSpringerOpenBoundary Value Problems1687-27702025-03-01202511910.1186/s13661-025-02030-wIntegral boundary value problems for second-order causal differential equationsWenli Wang0Junyan Bao1College of Management, Hebei UniversityCollege of Mathematics and Information Sciences, Hebei UniversityAbstract This paper is concerned with second-order causal differential equations with Riemann–Stieltjes integral boundary conditions. To obtain sufficient conditions for the existence of extremal solutions for such problems, a novel comparison principle is first formulated. Next, the existence and uniqueness of the solutions for the second-order linear differential equations are proved based on the fixed point theorem. Then, the monotone iterative technique is employed to investigate the existence of the extremal solution, with the relative results being derived on the basis of upper and lower solutions. Finally, an example is provided to verify the theoretical results.https://doi.org/10.1186/s13661-025-02030-wRiemann–Stieltjes integralBoundary value problemCausal operatorsExtremal solutions |
| spellingShingle | Wenli Wang Junyan Bao Integral boundary value problems for second-order causal differential equations Boundary Value Problems Riemann–Stieltjes integral Boundary value problem Causal operators Extremal solutions |
| title | Integral boundary value problems for second-order causal differential equations |
| title_full | Integral boundary value problems for second-order causal differential equations |
| title_fullStr | Integral boundary value problems for second-order causal differential equations |
| title_full_unstemmed | Integral boundary value problems for second-order causal differential equations |
| title_short | Integral boundary value problems for second-order causal differential equations |
| title_sort | integral boundary value problems for second order causal differential equations |
| topic | Riemann–Stieltjes integral Boundary value problem Causal operators Extremal solutions |
| url | https://doi.org/10.1186/s13661-025-02030-w |
| work_keys_str_mv | AT wenliwang integralboundaryvalueproblemsforsecondordercausaldifferentialequations AT junyanbao integralboundaryvalueproblemsforsecondordercausaldifferentialequations |