[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2012.20.4.533

EXISTENCE OF THE SOLUTIONS FOR THE ELLIPTIC PROBLEM WITH NONLINEAR TERM DECAYING AT THE ORIGIN

Choi, Q-Heung (Department of Mathematics Education Inha University)
Jung, Tacksun (Department of Mathematics Kunsan National University)

Publication Information

Korean Journal of Mathematics / v.20, no.4, 2012 , pp. 533-540 More about this Journal

Abstract

We consider the multiplicity of the solutions for the elliptic boundary value problem with $C^1$ nonlinear term decaying at the origin. We get a theorem which shows the existence of the nontrivial solution for the elliptic problem with $C^1$ nonlinear term decaying at the origin. We obtain this result by reducing the elliptic problem with the $C^1$ nonlinear term to the el-liptic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced the elliptic problem with bounded nonlinear term.

Keywords

Elliptic boundary value problem; nonlinear term decaying at the origin; bounded nonlinear term; variational method; critical point theory; mountain pass geometry; $(P.S.)_c$ condition;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
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