On positive solutions of functional-differential equations in banach spaces
<p/> <p>In this paper, we deal with two point boundary value problem (BVP) for the functional-differential equation of second order <inline-formula><graphic file="1029-242X-2001-507237-i1.gif"/></inline-formula> where the function <inline-formula><gra...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2001-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/6/507237 |
| _version_ | 1818943759713304576 |
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| author | Zima Mirosława |
| author_facet | Zima Mirosława |
| author_sort | Zima Mirosława |
| collection | DOAJ |
| description | <p/> <p>In this paper, we deal with two point boundary value problem (BVP) for the functional-differential equation of second order <inline-formula><graphic file="1029-242X-2001-507237-i1.gif"/></inline-formula> where the function <inline-formula><graphic file="1029-242X-2001-507237-i2.gif"/></inline-formula> takes values in a cone <inline-formula><graphic file="1029-242X-2001-507237-i3.gif"/></inline-formula> of a Banach space <inline-formula><graphic file="1029-242X-2001-507237-i4.gif"/></inline-formula>. For <inline-formula><graphic file="1029-242X-2001-507237-i5.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2001-507237-i6.gif"/></inline-formula> we obtain the BVP with reflection of the argument. Applying fixed point theorem on strict set-contraction from G. Li, <it>Proc. Amer. Math. Soc.</it> 97 (1986), 277–280, we prove the existence of positive solution in the space <inline-formula><graphic file="1029-242X-2001-507237-i7.gif"/></inline-formula>. Some inequalities involving <inline-formula><graphic file="1029-242X-2001-507237-i8.gif"/></inline-formula> and the respective Green's function are used. We also give the application of our existence results to the infinite system of functional–differential equations in the case <inline-formula><graphic file="1029-242X-2001-507237-i9.gif"/></inline-formula>.</p> |
| first_indexed | 2024-12-20T07:32:26Z |
| format | Article |
| id | doaj.art-a2eaba4dfd1240ba88af354cd443ad45 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-20T07:32:26Z |
| publishDate | 2001-01-01 |
| publisher | SpringerOpen |
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| series | Journal of Inequalities and Applications |
| spelling | doaj.art-a2eaba4dfd1240ba88af354cd443ad452022-12-21T19:48:23ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2001-01-0120013507237On positive solutions of functional-differential equations in banach spacesZima Mirosława<p/> <p>In this paper, we deal with two point boundary value problem (BVP) for the functional-differential equation of second order <inline-formula><graphic file="1029-242X-2001-507237-i1.gif"/></inline-formula> where the function <inline-formula><graphic file="1029-242X-2001-507237-i2.gif"/></inline-formula> takes values in a cone <inline-formula><graphic file="1029-242X-2001-507237-i3.gif"/></inline-formula> of a Banach space <inline-formula><graphic file="1029-242X-2001-507237-i4.gif"/></inline-formula>. For <inline-formula><graphic file="1029-242X-2001-507237-i5.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2001-507237-i6.gif"/></inline-formula> we obtain the BVP with reflection of the argument. Applying fixed point theorem on strict set-contraction from G. Li, <it>Proc. Amer. Math. Soc.</it> 97 (1986), 277–280, we prove the existence of positive solution in the space <inline-formula><graphic file="1029-242X-2001-507237-i7.gif"/></inline-formula>. Some inequalities involving <inline-formula><graphic file="1029-242X-2001-507237-i8.gif"/></inline-formula> and the respective Green's function are used. We also give the application of our existence results to the infinite system of functional–differential equations in the case <inline-formula><graphic file="1029-242X-2001-507237-i9.gif"/></inline-formula>.</p>http://www.journalofinequalitiesandapplications.com/content/6/507237Boundary value problem in a Banach spacePositive solutionConeFixed point theorem |
| spellingShingle | Zima Mirosława On positive solutions of functional-differential equations in banach spaces Journal of Inequalities and Applications Boundary value problem in a Banach space Positive solution Cone Fixed point theorem |
| title | On positive solutions of functional-differential equations in banach spaces |
| title_full | On positive solutions of functional-differential equations in banach spaces |
| title_fullStr | On positive solutions of functional-differential equations in banach spaces |
| title_full_unstemmed | On positive solutions of functional-differential equations in banach spaces |
| title_short | On positive solutions of functional-differential equations in banach spaces |
| title_sort | on positive solutions of functional differential equations in banach spaces |
| topic | Boundary value problem in a Banach space Positive solution Cone Fixed point theorem |
| url | http://www.journalofinequalitiesandapplications.com/content/6/507237 |
| work_keys_str_mv | AT zimamiros322awa onpositivesolutionsoffunctionaldifferentialequationsinbanachspaces |