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Existence of positive solutions for singular four-point boundary value problem with a p -Laplacian

Chunmei Miao, Junfang Zhao, Weigao Ge (2009)

Czechoslovak Mathematical Journal

In this paper we deal with the four-point singular boundary value problem ( φ p ( u ' ( t ) ) ) ' + q ( t ) f ( t , u ( t ) , u ' ( t ) ) = 0 , t ( 0 , 1 ) , u ' ( 0 ) - α u ( ξ ) = 0 , u ' ( 1 ) + β u ( η ) = 0 , where φ p ( s ) = | s | p - 2 s , p > 1 , 0 < ξ < η < 1 , α , β > 0 , q C [ 0 , 1 ] , q ( t ) > 0 , t ( 0 , 1 ) , and f C ( [ 0 , 1 ] × ( 0 , + ) × , ( 0 , + ) ) may be singular at u = 0 . By using the well-known theory of the Leray-Schauder degree, sufficient conditions are given for the existence of positive solutions.

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