A strongly nonlinear elliptic equation having natural growth terms and \(L^1\) data (Q1961253)

This paper deals with the Dirichlet problem for the equation \[ A(u)+g(x,u,\nabla u)=f \] in the setting of the Orlicz-Sobolev space \(W^1L_M(\Omega)\), where \(\Omega\) is a bounded open subset of \(\mathbb R^N\), \(A(u)=-\text{div}(a(x,u,\nabla u))\), \(f\in L^1(\Omega)\). Under the assumption that the \(N\)-function \(M\) satisfies the \(\Delta_2\) condition and under corresponding growth, coerciveness and monotonicity conditions on the functions \(a\) and \(g\) the authors prove the existence of a solution of the problem under consideration.