### Abstract

Several recent papers investigate the boundary value problem ϕ^{′′}(t)+λϕ^{′}(t)+ϕ(t)^{2}=0,t≥0subject 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.

Original language | English (US) |
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Pages (from-to) | 171-174 |

Number of pages | 4 |

Journal | Applied Mathematics Letters |

Volume | 68 |

DOIs | |

State | Published - Jun 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

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*Applied Mathematics Letters*, vol. 68, pp. 171-174. https://doi.org/10.1016/j.aml.2017.01.009

**A BVP nonexistence proof using Green's Theorem.** / Previte, Joseph P.; Paullet, Joseph E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A BVP nonexistence proof using Green's Theorem

AU - Previte, Joseph P.

AU - Paullet, Joseph E.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - Several recent papers investigate the boundary value problem ϕ′′(t)+λϕ′(t)+ϕ(t)2=0,t≥0subject 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 λmin∈[1,2∕3] such that solutions exist for λ≥λmin. It has been conjectured that for λ<λmin no solution exists. We improve existing results by proving that for λ<λ1≈.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.

AB - Several recent papers investigate the boundary value problem ϕ′′(t)+λϕ′(t)+ϕ(t)2=0,t≥0subject 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 λmin∈[1,2∕3] such that solutions exist for λ≥λmin. It has been conjectured that for λ<λmin no solution exists. We improve existing results by proving that for λ<λ1≈.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.

UR - http://www.scopus.com/inward/record.url?scp=85011874538&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011874538&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2017.01.009

DO - 10.1016/j.aml.2017.01.009

M3 - Article

AN - SCOPUS:85011874538

VL - 68

SP - 171

EP - 174

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -