Abstract We study elliptic equations with quasilinear perturbation { Δ u + 1 2 κ u Δ u 2 + e ∑ i , j = 1 N ( a i j ( u ) D i j u + 1 2 D z a i j ( u ) D i u D j u ) + f ( u ) + e h ( u ) = 0 , in Ω , u = 0 , on ∂ Ω , where Ω ⊂ R N , N ≥ 3 is a smooth bounded domain, κ ∈ { 0 , 1 } , e is a small parameter. Multiplicity result is proved by elliptic regularization method.

中文翻译：

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拟线性微扰椭圆方程的多重解

摘要 我们研究具有拟线性扰动的椭圆方程 { Δ u + 1 2 κ u Δ u 2 + e ∑ i , j = 1 N ( aij ( u ) D iju + 1 2 D zaij ( u ) D iu D ju ) + f ( u ) + eh ( u ) = 0 , in Ω , u = 0 , on ∂ Ω , 其中Ω ⊂ RN , N ≥ 3 是光滑有界域, κ ∈ { 0 , 1 } , e 是一个小参数。用椭圆正则化方法证明了多重性结果。