A Weak solutions for some variational nonlinear elliptic systems with multiple perturbations

Through Young measure, we handle variational quasilinear elliptic systems in both the divergence and perturbed forms of type $-\text{div}\,\big(\sigma(x,Du-\Upsilon(u))+ \phi(u)\big)+ \alpha(x) \mid u\mid^{p-2}u=f$ in $\Omega$, $u=0$ on $\partial\Omega$. Galerkin's method is utilized to obtain weak solutions $u$ within the framework of Sobolev spaces $W^{1,p}_0(\Omega;\R^m)$.