CMMSE: Maximal regularity and two-sided estimates of the approximation numbers of the nonlinear Sturm-Liouville equation solutions with rapidly oscillating coefficients in $L_{2} (R)$
• Mussakan Muratbekov,
• Serik Altynbek
Kazakh University of Economics Finance and International Trade

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Mussakan Muratbekov
Taraz State University named after M Kh Dulaty
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Serik Altynbek
Esil University
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## Abstract

A theorem on the maximum regularity of solutions of the nonlinear Sturm-Liouville equation with greatly growing and rapidly oscillating potential in the space $L_2(R)\,(R=(-\infty,\infty))$ is proved in this paper. Two-sided estimates of the Kolmogorov widths of the sets associated with solutions of the nonlinear Sturm-Liouville equation are also obtained. As is known, the obtained estimates given the opportunity to choose approximation apparatus that guarantees the maximum possible error.
24 Aug 2022Submitted to Mathematical Methods in the Applied Sciences
25 Aug 2022Submission Checks Completed
25 Aug 2022Assigned to Editor
26 Aug 2022Review(s) Completed, Editorial Evaluation Pending
27 Aug 2022Editorial Decision: Revise Major
05 Sep 2022Submission Checks Completed
05 Sep 2022Assigned to Editor
05 Sep 2022Reviewer(s) Assigned
29 Sep 2022Review(s) Completed, Editorial Evaluation Pending
27 Dec 2022Editorial Decision: Revise Minor