T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum
El Houssine Azroul ; Abdelkrim Barbara ; Meryem El Lekhlifi ; Mohamed Rhoudaf
Applicationes Mathematicae, Tome 39 (2012), p. 339-364 / Harvested from The Polish Digital Mathematics Library
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We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem -div(a(x,u,∇u))+g(x,u)=f-divF in Ω, where Ω is a bounded open domain of ℝN, N ≥ 2 and a:Ω×ℝ×ℝN→ℝN is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to ∏i=1NLp'(·)(Ω).

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:279953 
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     title = {T-p(x)-solutions for nonlinear elliptic equations with an L$^1$-dual datum},
     journal = {Applicationes Mathematicae},
     volume = {39},
     year = {2012},
     pages = {339-364},
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El Houssine Azroul; Abdelkrim Barbara; Meryem El Lekhlifi; Mohamed Rhoudaf. T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum. Applicationes Mathematicae, Tome 39 (2012) pp. 339-364. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-8/