In this paper we study the existence of solutions for the generated boundary value problem , with initial datum being an element of L 1 (Ω) + W −1,p where a(.) is a Carathéodory function satisfying the classical condition of type Leray-Lions hypothesis, while g(x, s, ξ) is a non-linear term which has a growth condition with respect to ξ and no growth with… (More)
In this paper, we study the existence of entropy solution for quasilinear elliptic equations of the form, for some right-hand side datum f in L 1 (Ω). Note that g(x, s, ξ) is a non-linear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s.(x)-solutions for nonlinear elliptic equations… (More)
We prove an existence result for a class of nonlinear parabolic systems. Without assumptions on the growth of some nonlinear terms, we prove the existence of a renormalized solution.