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具有对数项的choquard型问题解的存在性
首发时间：2025-03-14
摘要：本文研究了有界区域上一类具有对数非线性项的choquard型问题解的存在性。由于对数项既不满足单调性条件也不满足ambrosetti-rabinowitz条件,这给寻找该问题的弱解带来了额外的困难。在这个过程中,一个关键步骤是对对数项进行一些更加精细的估计。首先证明了能量泛函具有山路几何结构；其次证明了能量泛函具有收敛子列；再借助截断函数估计山路水平值；最后利用山路引理证明了该问题解的存在性。
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the existence of solutions for choquard-type problems with logarithmic perturbation
abstract：\justifying this paper investigates the existence of solutions for a class of choquard type problems with logarithmic nonlinear terms on a bounded domain. since the logarithmic term does not satisfy either the monotonicity condition or the ambrosetti-rabinowitz condition,this brings additional difficulties in searching for weak solutions to the problem.in this process,a key step is to conduct some more refined estimates on the logarithmic term.first,we prove that the energy functional possesses a mountain pass geometry.then,we show that the energy functional has a convergent subsequence.next,we estimate the mountain pass level by using a truncation function.finally,we prove the existence of solutions to the problem by employing the mountain pass lemma.
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具有对数项的choquard型问题解的存在性
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