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Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations
Journal of Fixed Point Theory and Applications ( IF 1.8 ) Pub Date : 2020-08-14 , DOI: 10.1007/s11784-020-00809-1
Farzaneh Pouladi Najafabadi , Juan J. Nieto , Hojjatollah Amiri Kayvanloo

First, we introduce a new measure of noncompactness in weighted Sobolev spaces \(W_{w}^{m,p}(\Omega )\), and then as an application, we study the existence of solutions for a class of the nonlinear convolution type integral equations using Darbo’s fixed point theorem associated with this new measure of noncompactness. Further, an example is presented to verify the effectiveness and applicability of our main results.

中文翻译:

加权Sobolev空间上非紧性的度量及其在非线性卷积型积分方程中的应用。

首先,我们引入了加权Sobolev空间\(W_ {w} ^ {m,p}(\ Omega)\)中的非紧致性的新度量,然后作为一种应用,我们研究了一类非线性问题的解的存在性卷积型积分方程,使用与这种新的非紧缩度量相关的Darbo不动点定理。此外,还提供了一个例子来验证我们主要结果的有效性和适用性。
更新日期:2020-08-14
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