Variational Integrals of a Class of Nonhomogeneous 𝒜 -Harmonic Equations

Abstract

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.