Existence of multiple positive solutions for one-dimensional p-Laplacian
By Youyu Wang, Chengmin Hou. 2006
112 citations recorded by the source corpus.
Abstract In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian ( ϕ p ( u ′ ) ) ′ + f ( t , u ) = 0 , t ∈ ( 0 , 1 ) , subject to the boundary value conditions: ϕ p ( u ′ ( 0 ) ) = ∑ i = 1 n − 2 a i ϕ p ( u ′ ( ξ i ) ) , u ( 1 ) = ∑ i = 1 n − 2 b i u ( ξ i ) , where ϕ p ( s ) = | s | p − 2 s , p > 1 , ξ i ∈ ( 0 , 1 ) with 0 ξ 1 ξ 2 ⋯ ξ n − 2 1 , and a i , b i satisfy a i , b i ∈ [ 0 , ∞ ] , 0 ∑ i = 1 n − 2 a i 1 , and ∑ i = 1 n − 2 b i 1 . Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/6621e10d209a14f36d17fd7ed66dd2d95f962fb1
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In Applied Mathematics
In Control and Systems Engineering
Citations in the corpus
- Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian☆ (2007, background): “The authors in [9,10] considered the multipoint BVP for one-dimensional p-Laplacian ( φp(u ′) )′ + f (t, u) = 0, t ∈ (0,1), (1.”