Search Results

In this work, we will prove the existence of bounded solutions for the nonlinear elliptic equations \(- div(a(x,u,\nabla u)) = g(x,u,\nabla u) -divf,\) in the setting of the weighted Sobolev space \(W^{1,p}(\Omega,w)\) where \(a\), \(g\) are Caratheodory functions which satisfy some conditions and \(f\) satisfies suitable summability assumption.

In this work, we shall be concerned with the existence of weak solutions of anisotropic elliptic operators \(Au +\sum_{i=1}^{N}g_{i}(x, u, \nabla u)+\sum_{i=1}^{N}H_{i}(x, \nabla u)=f-\sum_{i=1}^{N} \frac{\partial }{\partial x_{i}}k_{i}\) where the right hand side \(f\) belongs to \(L^{p^{'}_{\infty}}(\Omega)\) and \(k_{i}\) belongs to \(L^{p_{i}^{'}}(\Omega)\) for \(i=1,...,N\) and \(A\) is a Leray-Lions operator. The critical growth condition on \(g_{i}\) is…