A family of measures of noncompactness in the locally Sobolev spaces and its applications to some nonlinear Volterra integrodifferential equations

DOI10.1155/2018/3579079zbMath1493.47062OpenAlexW2791417468MaRDI QIDQ2337098

H. Mehravaran, Mahnaz Khanehgir, Reza Allahyari

Publication date: 19 November 2019

Published in: Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/3579079

zbMATH Keywords

nonlinear Volterra integrodifferential equationsfamily of measures of noncompactnesslocally Sobolev spaces

Mathematics Subject Classification ID

Volterra integral equations (45D05) Measures of noncompactness and condensing mappings, (K)-set contractions, etc. (47H08)

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Measures of noncompactness in the space of regulated functions \(R (J, \mathbb{R}^{\infty})\) and its application to some nonlinear Infinite systems of fractional differential equations

Cites Work

• The existence of fixed points via the measure of noncompactness and its application to functional-integral equations
• The Kolmogorov-Riesz compactness theorem
• Measures of weak noncompactness and nonlinear integral equations of convolution type
• Functional analysis, Sobolev spaces and partial differential equations
• Elliptic partial differential equations of second order
• Construction of measures of noncompactness of \(C^k(Omega)\) and \(C^k_0\) and their application to functional integral-differential equations
• A family of measures of noncompactness in the space \(L^1_{\mathrm{loc}}(\mathbb R_+)\) and its application to some nonlinear Volterra integral equation
• Absolute continuity on tracks and mappings of Sobolev spaces
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