Abstract
This paper presents the existence of positive solutions for the singular three-point boundary value problem u ″ ( t ) + a ( t ) u ′ ( t ) + b ( t ) u ( t ) + h ( t ) f ( t , u ) = 0 , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = α u ( η ) , where h ( t ) is allowed to be singular at t = 0 , 1 and f may be singular at u = 0. The existence criteria for positive solutions of the above problem is established by applying the fixed point index theorem under some weaker conditions concerning the first eigenvalue corresponding to the relevant linear operator.
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