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山路引理在一类渐近线性椭圆方程中的应用

, PP. 145-149

Keywords: Dirichlet问题,山路引理,渐近线性

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Abstract:

研究了形如-△u=λa(x)u+f(x,u)的Dirichlet问题的解的存在性,其中x∈Ω,u∈H10(Ω),a(x)为非负且绝对可积函数,f(x,t)∈C(Ω×R),f(x,t)t关于t单调不减,且f(x,t)关于t在无穷远处是渐近线性的.在没有(ARAmbrosettiA,RabinowitzPH.JFunctAnal,1973,14139ˉ381.)条件的情况下定义了一个约束变分问题,通过一种改进了的山路引理,证明了这类方程的正解存在性问题.

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