Variational Integrals of a Class of Nonhomogeneous A-Harmonic Equations

We introduce a class of variational integrals whose Euler equations are nonhomogeneous A-harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous A-harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.