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T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

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Azroul E., Barbara A., El Lekhlifi M., Rhoudaf M.

Applicationes Mathematicae

2012

tom 39

nr 3

339-364

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 $ℝ^{N}$, N ≥ 2 and $a: Ω × ℝ× ℝ^{N} → ℝ^{N}$ 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 $∏_{i=1}^{N}L^{p'(·)}(Ω)$.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Azroul E.

1 Barbara A.

1 El Lekhlifi M.

1 Rhoudaf M.

1 2012

Wyniki wyszukiwania

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum