### Abstract

This paper is concerned with semilinear tow-point boundary value problems of the form -(p(x)u′)′ + f(x, u) = 0, a ≤ x ≤ b, α_{0}u(a) - α_{1}u′(a) = α, β_{1}u′(b) + β,_{1}u′(b) = β, α_{i} ≥ 0, β_{i}≥ 0, i = 0, 1, α_{0}+α_{1} > 0, β_{0}+β _{1} > 0, α_{0}+β_{0} > 0. Under the assumption inf f_{u} > -λ_{1}, where λ_{1} is the smallest eigenvalue of u = -(pu′)′ with the boundary conditions, unique existence theorems of solution for the continuous problem and a discretized system with not necessarily uniform nodes are given as well as error estimates. The results generalize three theorems of Lees for u″ = f(x, u), 0 ≤ x ≤ 1, u(0) = α, u(1) = β.

Original language | English |
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Pages (from-to) | 293-313 |

Number of pages | 21 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 23 |

Issue number | 3 |

Publication status | Published - 2006 Oct |

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### Keywords

- Discretization
- Error estimates
- Existence of solution
- Theorems of Lees
- Tow-point boundary value problems

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics