Quasilinear degenerated equations with L^1 datum and without coercivity in perturbation terms
L. Aharouch, Department of Mathematics, Faculty of Sciences of Fez, Fez, Morocco E. J. Qualitative Theory of Diff. Equ., No. 19. (2006), pp. 1-18.
E. Azroul, Department of Mathematics, Faculty of Sciences of Fez, Fez, Morocco
A. Benkirane, Department of Mathematics, Faculty of Sciences of Fez, Fez, Morocco
| Communicated by J. Mawhin. | Received on 2005-10-15 Appeared on 2006-11-15 |
Abstract: In this paper we study the existence of solutions for the generated boundary value problem, with initial datum being an element of $L^1(\Omega)+W^{-1, p'}(\Omega, w^{*})$
$$-{\rm div}a(x, u, \nabla u) + g(x, u, \nabla u) = f-{\rm div}F $$
where $a(.)$ is a Carath\'eodory function satisfying the classical condition of type Leray-Lions hypothesis, while $g(x, s, \xi)$ is a non-linear term which has a growth condition with respect to $\xi$ and no growth with respect to $s$, but it satisfies a sign condition on $s$.
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