Abstract

In this paper, we prove the existence of multiple solutions for second order Sturm–Liouville boundary value problem { − L u = f ( x , u ) , x ∈ [ 0 , 1 ] R 1 ( u ) = 0 , R 2 ( u ) = 0 , where L u = ( p ( x ) u ′ ) ′ − q ( x ) u is a Sturm–Liouville operator, R 1 ( u ) = α u ′ ( 0 ) − β u ( 0 ) , R 2 ( u ) = γ u ′ ( 1 ) + σ u ( 1 ) . The technical approach is fully based on lower and upper solutions and variational methods. The interesting point is that the existence of four solutions and seven solutions is given.

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