Eigenvalue criteria for existence of multiple positive solutions to boundary value problems of second-order delay differential equations

Abstract

Criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second-order delay differential equations of the form { − ( p ( t ) y ′ ( t ) ) ′ + q ( t ) y ( t ) = f ( t , y ( t − τ ) , y ( t + a ) ) , t ∈ ( 0 , 1 ) , α y ( t ) − β y ′ ( t ) = η ( t ) , t ∈ [ − τ , 0 ] , γ y ( t ) + δ y ′ ( t ) = ξ ( t ) , t ∈ [ 1 , 1 + a ] , where 0 < τ , a < 1 / 4 are suitably small, p ∈ C 1 [ 0 , 1 ] , p > 0 , q ∈ C [ 0 , 1 ] , and q ⩾ 0 .