Existence of a Nontrivial Solution for a Class of Superquadratic Elliptic Problems ()
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.
DOI: 10.4236/apm.2012.25043
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Abstract
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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