Resonant singular boundary value problems
O'Regan, Donal
O'Regan, Donal
Publication Date
1995-12-01
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Article
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O'Regan, Donal (1995). Resonant singular boundary value problems. Rocky Mountain Journal of Mathematics 25 (4), 1459-1475
Abstract
Existence theory is developed for the ''resonant'' singular problem (1/(pq))(py')' + lambda(0)y = f(t,y,py') almost everywhere on [0, 1] with lim(t-->0+) p(t)y'(t) = ay(1) + blim(t-->1-) p(t)y'(t) = 0. Here lambda(0) is the first eigenvalue of (1/(pq))(pu')' + lambda u = 0 almost everywhere on [0,1] with lim(t-->0+) p(t)u'(t) = au(1) + blim(t-->1-) p(t)u'(t) = 0. We do not assume integral(0)(1) ds/p(s) < infinity in this paper.
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Rocky Mountain Mathematics Consortium
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Attribution-NonCommercial-NoDerivs 3.0 Ireland