Existence Result for Solutions to Some Noncoercive Elliptic Equations

In this work, we study a class of degenerate Dirichlet problems, whose prototype is { − div ( ∇ u ( 1 + | u | ) γ + c ( x ) | u | θ − 1 u log β ( 1 + | u | ) ) = f in Ω , u = 0 on ∂ Ω , where Ω is a bounded open subset of R N . 0 < γ < 1 , 0 < θ ≤ 1 and 0 ≤ β < 1 . We prove existence of bounded solutions when f and c belong to suitable Lebesgue spaces. Moreover, we investegate the existence of renormalized solutions when the function f belongs only to L 1 ( Ω ) .