Variational Integrals of a Class of Nonhomogeneous ? -Harmonic Equations

Abstract EN

We introduce a class of variational integrals whose Euler equations are nonhomogeneous ? -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 ? -harmonic equations by applying direct methods of the calculus of variations.

Besides, we establish some interesting results on variational integrals.