A BVP nonexistence proof using Green's Theorem. (June 2017) - Previte, Joseph P.
Abstract: Several recent papers investigate the boundary value problem ϕ ′ ′ ( t ) + λ ϕ ′ ( t ) + ϕ ( t ) 2 = 0, t ≥ 0 subject to ϕ ( 0 ) = 1, ϕ ( ∞ ) = 0, which arises in certain situations of boundary layer flow. Previous work on the problem established the existence of a λ min ∈ [ 1, 2 ∕ 3 ] such that solutions exist for λ ≥ λ min . It has been conjectured that for λ < λ min no solution exists. We improve existing results by proving that for λ < λ 1 ≈ . 96105 no solution to the boundary value problem exists. The proof employs a novel application of Green's Theorem and is applicable to other boundary value problems.