## Abstract

A family of nonlinear elliptic boundary value problems, affected by the presence of two positive parameters λ and ε, is considered. These problems arise in the theoretical treatment of membranes with enzymic activity, ε being in several realistic situations a small parameter compared to λ. We give an appropriate formulation of the reduced problem which corresponds to ε = 0. On the other hand there exists a critical value λ_{C} of λ such that for λ ≤ λ_{C} the problems with ε > 0 are regular and for λ > λ_{C} singular perturbations of the reduced problem. Some estimates for λ_{C} as a functional of the boundary function ϕ are derived and an explicit formula for the first variation of λ_{C} with respect to ϕ is established. Newton-Kantorovich iterative procedure is applied in order to approximate the solutions and to derive some asymptotic formulae. This procedure gives rise to an interesting class of linear coercive singular perturbations with discontinuous coefficients.

Original language | English |
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Pages (from-to) | 289-303 |

Number of pages | 15 |

Journal | North-Holland Mathematics Studies |

Volume | 47 |

Issue number | C |

DOIs | |

Publication status | Published - 1 Jan 1981 |

Externally published | Yes |