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Eigenvalue Criteria for Existence of a Positive Solution to a Singular Three Point BVP

Volume 2, Number 2 (2012), 48 - 55

Eigenvalue Criteria for Existence of a Positive Solution to a Singular Three Point BVP

Communicated By: 
Enrique Zuazua
Price: $20.00

Abstract

Under suitable conditions we provide nonexistence and existence results for a positive solution to the singular three point boundary value problem ( −(au0)0 (t) = b(t) f (t,u(t)), t 2 (0, 1), u0(0) = 0, u(1) = u(), where , 2 (0, 1), a,b 2 C((0, 1), [0,+1)), a > 0 in (0, 1), 1 a is integrable on any compact subset of (0,1], b does not vanish identically and is integrable on any compact subset of [0,1) and f : [0, 1]×[0,+1)![0,+1) is continuous.