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http://dx.doi.org/10.11568/kjm.2013.21.2.117

NONTRIVIAL SOLUTION FOR THE BIHARMONIC BOUNDARY VALUE PROBLEM WITH SOME NONLINEAR TERM  

Jung, Tacksun (Department of Mathematics Kunsan National University)
Choi, Q-Heung (Department of Mathematics Education Inha University)
Publication Information
Korean Journal of Mathematics / v.21, no.2, 2013 , pp. 117-124 More about this Journal
Abstract
We investigate the existence of weak solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We get a theorem which shows the existence of nontrivial solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We obtain this result by reducing the biharmonic problem with nonlinear term to the biharmonic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced biharmonic problem with bounded nonlinear term.
Keywords
Biharmonic boundary value problem; nonlinear term decaying at the origin; bounded nonlinear term; variational method; critical point theory; mountain pass geometry; (PS) condition;
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