• Korean Journal of Mathematics
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• 제22권2호
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• pp.355-365
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• 2014

We show the existence of nontrivial solutions for some fourth order elliptic boundary value problem with fully nonlinear term. We obtain this result by approaching the variational method and using a linking theorem. We also get a uniqueness result.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.633-644
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• 2014

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

• Proceedings of the Jangjeon Mathematical Society
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• 제20권2호
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• pp.183-191
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• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• 한국수학사학회지
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• 제16권4호
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• pp.107-115
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• 2003

The nonlinear fourth order elliptic equations with jumping nonlinearity was modeled by McKenna. We investigate the trends for the researches of the existence of solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary Condition, ${\Delta}^2u{＋}c{\Delta}u=b_1[(u＋1)^{-}1]{＋}b_2u^+$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.323-334
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• 2010

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.455-468
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• 2017

We prove the existence of multiple solutions for the fourth order nonlinear elliptic problem with fully nonlinear term. Our method is based on the critical point theory; the variation of linking method and category theory.