On a non linear partial differential equation having natural growth terms and unbounded solution

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)347-364
Journal / PublicationAnnales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
Volume5
Issue number4
Publication statusPublished - 1 Jul 1988
Externally publishedYes

Abstract

We prove the existence of a solution of the nonlinear elliptic equation: A(u) + g(x, u, Du) = h(x), where A is a Leray-Lions operator from W0 1,p(Ω) into W−1, p′(Ω) and g is a nonlinear term with “natural” growth with respect to Du [i.e. such that |g(x, u, ξ)| ≦ b(|u|) (|ξ|p + c(x))], satisfying the sign condition g(x, u, ξ)u ≧ 0 but no growth condition with respect to u. Here h belongs to W−1, p′(Ω), thus the solution u of the problem does not in general be more smooth than W0 1,p(Ω). The existence of a solution is also proved for the corresponding obstacle problem.

Research Area(s)

  • 35 J 20, 35 J 65, 35 J 85, 47 H 15, 49 A 29

Bibliographic Note

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Citation Format(s)

On a non linear partial differential equation having natural growth terms and unbounded solution. / Bensoussan, A.; Boccardo, L.; Murat, F.

In: Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, Vol. 5, No. 4, 01.07.1988, p. 347-364.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review