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.
Guanfeng Li. Yong Wang. Gejun Bao. "Variational Integrals of a Class of Nonhomogeneous -Harmonic Equations." Abstr. Appl. Anal. 2014 (SI33) 1 - 10, 2014. https://doi.org/10.1155/2014/697974