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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).