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- W2032912448 abstract "We study nonlinear boundary value problems of the form y ′ = g ( t , y ) f ( y ′), y ′(0) = m ≤ 0, y (1) = 0, where g > 0 on [0, 1) × (0, ∞), f < 0 on ( m 0 , m 1 ), m 0 < m < m 1 , and f ( m o ) = 0. We specifically allow g to be singular in t at t = 1 and f to be singular in y at y = 0. We provide conditions under which the boundary value problem has a unique positive solution, which then satisfies m o < y ′( t ) ≤ m . We also obtain information about the qualitative behavior of this solution as t → 1 − . For example, we distinguish cases for which lim t → 1 − y ′( t ) either equals m o or is greater than m o , and obtain asymptotic formulae for y ( t ) and y ′( t ) as t → 1 − ." @default.
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- W2032912448 date "2000-09-01" @default.
- W2032912448 modified "2023-09-23" @default.
- W2032912448 title "A class of singular nonlinear boundary value problems" @default.
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- W2032912448 doi "https://doi.org/10.1016/s0895-7177(00)00160-6" @default.
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