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ON THE CONNECTION BETWEEN TWO QUASILINEAR ELLIPTIC PROBLEMS WITH SOURCE TERMS OF ORDER 0 OR 1

HAYDAR ABDEL HAMID

Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Faculté des Sciences, 37200 Tours, France

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and

MARIE FRANÇOISE BIDAUT-VERON

Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Faculté des Sciences, 37200 Tours, France

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https://doi.org/10.1142/S0219199710003993Cited by:26 (Source: Crossref)

Abstract

We establish a precise connection between two elliptic quasilinear problems with Dirichlet data in a bounded domain of ℝ^N. The first one, of the form

involves a source gradient term with natural growth, where β is non-negative, λ > 0, f(x) ≧ 0, and α is a non-negative measure. The second one, of the form

presents a source term of order 0, where g is non-decreasing, and μ is a non-negative measure. Here β and g can present an asymptote. The correlation gives new results of existence, non-existence, regularity and multiplicity of the solutions for the two problems, without or with measures. New informations on the extremal solutions are given when g is superlinear.

Keywords:

AMSC: 35J92, 35B65, 35D05, 35D10, 35B38

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