Abstract

We consider the multiplicity of the solutions for the elliptic boundary value problem with <TEX>$C^1$</TEX> nonlinear term decaying at the origin. We get a theorem which shows the existence of the nontrivial solution for the elliptic problem with <TEX>$C^1$</TEX> nonlinear term decaying at the origin. We obtain this result by reducing the elliptic problem with the <TEX>$C^1$</TEX> 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.

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