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- W2059276309 abstract "Let ϕ and θ be two increasing homeomorphisms from R onto R with ϕ ( 0 ) = 0 , θ ( 0 ) = 0 . Let f : [ 0 , 1 ] × R × R ↦ R be a function satisfying Carathéodory's conditions, and for each i , i = 1 , 2 , … , m − 2 , let a i : R ↦ R , be a continuous function, with ∑ i = 1 m − 2 a i ( 0 ) = 1 , ξ i ∈ ( 0 , 1 ) , 0 < ξ 1 < ξ 2 < ⋯ < ξ m − 2 < 1 . In this paper we first prove a suitable continuation lemma of Leray–Schauder type which we use to obtain several existence results for the m -point boundary value problem: ( ϕ ( u ′ ) ) ′ = f ( t , u , u ′ ) , t ∈ ( 0 , 1 ) , u ′ ( 0 ) = 0 , θ ( u ( 1 ) ) = ∑ i = 1 m − 2 θ ( u ( ξ i ) ) a i ( u ′ ( ξ i ) ) . We note that this problem is at resonance , in the sense that the associated m -point boundary value problem ( ϕ ( u ′ ( t ) ) ) ′ = 0 , t ∈ ( 0 , 1 ) , u ′ ( 0 ) = 0 , θ ( u ( 1 ) ) = ∑ i = 1 m − 2 θ ( u ( ξ i ) ) a i ( u ′ ( ξ i ) ) has the non-trivial solution u ( t ) = ρ , where ρ ∈ R is an arbitrary constant vector, in view of the assumption ∑ i = 1 m − 2 a i ( 0 ) = 1 ." @default.
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- W2059276309 date "2007-09-01" @default.
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- W2059276309 title "Some multipoint boundary value problems of Neumann–Dirichlet type involving a multipoint p-Laplace like operator" @default.
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- W2059276309 doi "https://doi.org/10.1016/j.jmaa.2006.09.054" @default.
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