Author(s)

Xiuming Mo, Ping Jing, Yan Zhao, Anmin Mao

Department of Biotechnology, Beijing City University, Beijing, China.
Employee’s College of Dongcheng in Beijing, Beijing, China.
School of Mathematical Sciences, Qufu Normal University, Shandong, China.
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China.

We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a Hilbert space via the local linking theorem. Different from the works in the literature, the new theorem is constructed under the(C)* condition instead of (PS)* condition.

Elliptic Problems; Local linking Theorem; (C)* Condition; Superquadratic

X. Mo, P. Jing, Y. Zhao and A. Mao, "Existence of a Nontrivial Solution for a Class of Superquadratic Elliptic Problems," Advances in Pure Mathematics, Vol. 2 No. 5, 2012, pp. 314-317. doi: 10.4236/apm.2012.25043.