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Existence of positive solutions for boundary-value problems with singularities in phase variables

Agarwal, Ravi P.
; 
ORegan, Donal
; 
Stank, Svatoslav
Repository DOI
Publication Date
2004-02-01
Keywords
singular boundary-value problem, mixed condition, positive solution, topological transversality theorem
Type
Article
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Citation
Agarwal, Ravi P. ORegan, Donal; Stank, Svatoslav (2004). Existence of positive solutions for boundary-value problems with singularities in phase variables. Proceedings of the Edinburgh Mathematical Society 47 , 1-13
Abstract
The singular boundary-value problem (g(x'))' = muf(t,x,x'), x'(0) = 0, x(T) = b > 0 is considered. Here mu is the parameter and f(t,x,y), which satisfies local Caratheodory conditions on [0, T] x (R \ {b}) x (R \ {0}), may be singular at the values x = b and y = 0 of the phase variables x and y, respectively. Conditions guaranteeing the existence of a positive solution to the above problem for suitable positive values of mu are given. The proofs are based on regularization and sequential techniques and use the topological transversality theorem.
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Publisher
Cambridge University Press (CUP)
Publisher DOI
10.1017/s0013091503000105
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
cbn
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Externally hosted open access publications with University of Galway authors (1)