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 |
| Summary: | <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> |
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| ISSN: | 1025-5834 1029-242X |