涉及散度形式一般算子的椭圆方程弱解的存在性

IF 0.4 Q4 MATHEMATICS Matematicki Vesnik Pub Date : 2023-01-01 DOI:10.57016/mv-kg8494sm

S. Amirkhanlou, G. Afrouzi, L. Beznea

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引用次数: 0

摘要

在rn的光滑有界区域上，在Dirichlet边界条件下，建立了一类具有散度形式的一般算子的椭圆型方程至少两个不同弱解的存在性。利用可微泛函的一个临界点结果，证明了该问题至少存在两个不同的非平凡弱解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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EXISTENCE OF ONE WEAK SOLUTION FOR ELLIPTIC EQUATIONS INVOLVING A GENERAL OPERATOR IN DIVERGENCE FORM

In this paper, we establish the existence of at least two distinct weak solutions for a class of elliptic equations involving a general operator in divergence form, subject to Dirichlet boundary conditions in a smooth bounded domain in R N . A critical point result for diﬀerentiable functionals is exploited, in order to prove that the problem admits at least two distinct non-trivial weak solutions.

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