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Abstract and Applied Analysis
Volume 2014, Article ID 697974, 10 pages
http://dx.doi.org/10.1155/2014/697974
Research Article

Variational Integrals of a Class of Nonhomogeneous -Harmonic Equations

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 20 September 2013; Accepted 10 January 2014; Published 27 February 2014

Academic Editor: Shusen Ding

Copyright © 2014 Guanfeng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.