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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 1999, 4(1), 69-74; https://doi.org/10.3390/mca4010069

On the Theory of Generalized Ballistical Problem for Nonlinear Abstract Differential Equations

Osinangazi University, Faculty of Engineering & Architecture 26480 Bati Meselik, Eskisehir, Turkey
Published: 1 April 1999
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Abstract

In the present work, we have obtained principally new results for solvability and non-solvability of one problem for second order abstract differential equations with the main linear part. The method, based on solving corresponding Dirichlet problem, lies on the basis of present investigations. In section 1, we present the formulation of the basic problem and reduce the short review of same investigations related to given problems. In section 2, we show the roll of the corresponding subsidiary boundary value problem for linear equation in the study of the basic problem. In section 3, we present the theorems of existence and nonexistence of the solution of the ballistical problem for nonlinear abstract differential equations with the linear part, in the case when the initial and the latter points of the desired solutions are not coinciding. Also we can prove the theorems of solvabilitv and non-solvability of considering problem in the case, when the Initial and the latter points desired trajectory are coinciding.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Shamilov, A.K. On the Theory of Generalized Ballistical Problem for Nonlinear Abstract Differential Equations. Math. Comput. Appl. 1999, 4, 69-74.

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