Strongly nonlinear elliptic variational unilateral problems in Orlicz space. (2006) - Aharouch, L.; Benkirane, A.; Rhoudaf, M.
Abstract : We will be concerned with the existence result of unilateral problem associated to the equations of the form A u + g ( x, u, ∇ u ) = f, where A is a Leray-Lions operator from its domain D ( A ) ⊂ W 0 1 L M ( Ω ) into W − 1 E M ¯ ( Ω ) . On the nonlinear lower order term g ( x, u, ∇ u ), we assume that it is a Carathéodory function having natural growth with respect to | ∇ u |, and satisfies the sign condition. The right-hand side f belongs to W − 1 E M ¯ ( Ω ) .