Existence of a Nontrivial Solution for a Class of Superquadratic Elliptic Problems

DOI: 10.4236/apm.2012.25043   PDF   HTML     2,666 Downloads   5,026 Views  

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.

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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.

References

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