Abstract
In this paper, we study the second-order three-point boundary value problem with a p -Laplacian operator { ( ϕ p ( x ′ ( t ) ) ) ′ + g ( x ( t ) ) = f ( t , x ( t ) , x ′ ( t ) ) , x ( 0 ) = 0 , x ( ξ ) = β x ( 1 ) , where ϕ p ( s ) = | s | p − 2 s , p > 1 , ξ ∈ ( 0 , 1 ) , β ∈ ( 0 , 1 ) ⋃ ( 1 , ∞ ) . We obtain sufficient conditions for the existence of multiple solutions by applying generalized polar coordinates and the Leray–Schauder degree theorem.
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