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Titlebook: Differential and Integral Inequalities; Wolfgang Walter Book 1970 Springer-Verlag Berlin Heidelberg 1970 Banach Space.Differentialungleich

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发表于 2025-3-21 16:56:00 | 显示全部楼层 |阅读模式
书目名称Differential and Integral Inequalities
编辑Wolfgang Walter
视频video
丛书名称Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
图书封面Titlebook: Differential and Integral Inequalities;  Wolfgang Walter Book 1970 Springer-Verlag Berlin Heidelberg 1970 Banach Space.Differentialungleich
描述In 1964 the author‘s mono graph "Differential- und Integral-Un­ gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs­ und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book. In the meantime the literature on differential and integral in­ equalities increased greatly. We have tried to incorporate new results as far as possible. As a matter of fact, the Bibliography has been almost doubled in size. The most substantial additions are in the field of existence theory. In Chapter I we have included the basic theorems on Volterra integral equations in Banach space (covering the case of ordinary differential equations in Banach space). Corresponding theorems on differential inequalities have been added in Chapter II. This was done with a view to the new sections; dealing with the line method, in the chapter on parabolic differential equations. Section 35 contains an exposition of this method in connection with estimation and convergence. An existence theory for the general nonlinear parabolic equation in one space variable based on the line method is given in Section 36. This theory is c
出版日期Book 1970
关键词Banach Space; Differentialungleichung; Inequalities; Integral; Integralungleichung; differential equation
版次1
doihttps://doi.org/10.1007/978-3-642-86405-6
isbn_softcover978-3-642-86407-0
isbn_ebook978-3-642-86405-6
copyrightSpringer-Verlag Berlin Heidelberg 1970
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Ordinary Differential Equations,ld subject, this will be justified by a new method. This method deals with . equations and inequalities, whereas earlier the corresponding . equations stood in the foreground. This is not done merely to give the old theorems a second proof. Rather, both of these first two chapters furnish, besides t
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Volterra Integral Equations in Several Variables Hyperbolic Differential Equations,with a completeness similar to that for ordinary differential equations in the first two chapters. If it is approached with the methods of the first chapter, this problem leads to Volterra integral equations in two variables which can be handled largely as in the one-dimensional case; even considera
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Parabolic Differential Equations,is notation expresses the fact that the independent variables fall into two essentially different groups. The scalar variable . is also called the “time” variable, the variable . ∈ . the “space” variable. We note that another .-dimensional space will occur later for parabolic systems. In order to di
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Volterra Integral Equations in Several Variables Hyperbolic Differential Equations,hapter, this problem leads to Volterra integral equations in two variables which can be handled largely as in the one-dimensional case; even consideration of such integral equations in an arbitrary number . of independent variables produces no new difficulties. A significant part of the present chapter is devoted to the development of this theory.
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https://doi.org/10.1007/978-1-4684-2331-0nce problem; (β) the uniqueness problem and the related problem of continuous dependence on the various given data; (γ) qualitative and quantitative properties of the solution (e.g., statements about monotonicity or convexity of the solution, validity of the maximum principle,..., numerical determination of the solution).
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