<it>A priori</it> estimates for the existence of a solution for a multi-point boundary value problem
<p/> <p>Let <inline-formula><graphic file="1029-242X-2000-857065-i1.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2000-857065-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-200...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2000-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/5/857065 |
| Summary: | <p/> <p>Let <inline-formula><graphic file="1029-242X-2000-857065-i1.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2000-857065-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2000-857065-i3.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2000-857065-i4.gif"/></inline-formula>, with <inline-formula><graphic file="1029-242X-2000-857065-i5.gif"/></inline-formula> be given. Let <inline-formula><graphic file="1029-242X-2000-857065-i6.gif"/></inline-formula> be such that <inline-formula><graphic file="1029-242X-2000-857065-i7.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2000-857065-i8.gif"/></inline-formula> be given. This paper is concerned with the problem of obtaining Poincaré type a <it>priori</it> estimates of the form <inline-formula><graphic file="1029-242X-2000-857065-i9.gif"/></inline-formula>. The study of such estimates is motivated by the problem of existence of a solution for the Caratheodory equation <inline-formula><graphic file="1029-242X-2000-857065-i10.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2000-857065-i11.gif"/></inline-formula>, satisfying boundary conditions <inline-formula><graphic file="1029-242X-2000-857065-i12.gif"/></inline-formula>. This problem was studied earlier by Gupta <it>et al. (Jour. Math. Anal. Appl.</it> 189 (1995), 575–584) when the <inline-formula><graphic file="1029-242X-2000-857065-i13.gif"/></inline-formula>'s, all had the same sign.</p> |
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| ISSN: | 1025-5834 1029-242X |