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Existence of a Nontrivial Solution for a Class of Superquadratic Elliptic Problems
Department of Biotechnology, Beijing City University, Beijing, China
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
Employee’s College of Dongcheng in Beijing, Beijing, China
School of Mathematical Sciences, Qufu Normal University, Shandong, China
- 1 Department of Biotechnology, Beijing City University, Beijing, China
- 2 School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
- 3 Employee’s College of Dongcheng in Beijing, Beijing, China
- 4 School of Mathematical Sciences, Qufu Normal University, Shandong, China
Advances in Pure Mathematics·Volume 02 (2012)·Pages 314–317·Published 25 September 2012·DOI10.4236/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.
KeywordsElliptic ProblemsLocal linking Theorem<i>(C)</i>* ConditionSuperquadratic
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