We study weakly perturbed integrodifferential equations with degenerate kernel in Banach spaces and establish conditions for the bifurcation of solutions of weakly perturbed integrodifferential ...equations in Banach spaces at the point
ε
= 0. A convergent iterative procedure is proposed for the determination of solutions in the form of series
∑
i
=
1
+
∞
ε
i
z
i
t
in powers of
ε
..
We prove theorems on the general form of generalized invertible operators in Banach spaces in the case where the operators are topologically Noetherian or topologically Fredholm. These theorems ...generalize the well-known Nikol’skii theorem on the general form of Fredholm operators and the Atkinson theorem on the general form of Noetherian operators in function spaces.
We establish conditions required for the generalized invertibility of Fredholm integral operators with degenerate kernels in Banach spaces. New results on the generalized inversion of Fredholm ...integral operators with degenerate kernels in Banach spaces are obtained. A detailed analysis of an example is also presented.
Bounded Solutions of Evolutionary Equations Boichuk, O. A.; Zhuravl’ov, V. P.; Pokutnyi, O. O.
Ukrainian mathematical journal,
06/2018, Letnik:
70, Številka:
1
Journal Article
Recenzirano
We study the problems of existence and representations of the solutions bounded on the entire axis for both linear and nonlinear differential equations with unbounded operator coefficients in the ...Fréchet and Banach spaces under the condition of exponential dichotomy on the semiaxes of the corresponding homogeneous equation.
The aim is to carry out the analysis of the disease incidence of students and to scientifically substantiate the directions of improving health and fitness activity in the physical education of the ...students of special medical groups.
Materials and methods: The study was conducted at Zhytomyr National Agroecological University in 1992-2019. The main pedagogical experiment involved 681 students (209 males and 472 females, aged 17-22). The research methods included theoretical methods (the analysis and synthesis of literary sources, the analysis of curricula, the assessment of the quality of classes with the students of special medical groups, the study and analysis of the medical cards of students); empirical methods (pedagogical observations, the methods of mathematical statistics).
Results: The study determined that more than 57.6 % students of higher educational establishments of Ukraine had an unsatisfactory level of physical fitness, significant physical disabilities, diseases; from 10.9 to 20.5 % students had an insufficient level of physical fitness and significant health disorders; from 8.1 to 17.4 % students belongedto a special medical group; from 0.4 to 1.2 % students were exempt from sports and had chronic diseases and disabilities.
Conclusions: The quality of the physical education process in special medical groups depends on the interconnection of all the components that affect its efficiency, including an outlook, motives, interests, the attitude of students to physical education and health-improving activities; the students' desire to overcome their health disabilities; individualcharacteristics of students; the means, forms, methods, and principles of physical self-improvement; material and technical support of educational and health and fitness events.
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