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Differential equations

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Articles 121 - 126 of 126

Full-Text Articles in Mathematics

On The Existence Of Solutions Of Differential Equations And Zeros Of Operators In K-Banach Spaces, Evin Bronson, R. L. Tennison, A. Richard Mitchell Jan 1975

On The Existence Of Solutions Of Differential Equations And Zeros Of Operators In K-Banach Spaces, Evin Bronson, R. L. Tennison, A. Richard Mitchell

Mathematics Technical Papers - Archive

The theory of existence of solutions of differential equations in a Banach space employing norm as a measure is sufficiently well known [5, 6, 8, 9]. Also utilizing this theory one can prove the existence of zeros of operators [2, 7, 8, 9, 11]. The advantage of using a generalized norm as a candidate in discussing the qualitative theory of differential equations is also known [1]. These thoughts naturally lead to the use of cone-valued norms as a measure since this approach unifies the existing theories as well as offers a more flexible mechanism for applications. In this paper, we …

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A New Approach To The Method Of Nonlinear Variation Of Parameters, A. Richard Mitchell, M. E. Lord Jan 1975

A New Approach To The Method Of Nonlinear Variation Of Parameters, A. Richard Mitchell, M. E. Lord

Mathematics Technical Papers - Archive

As is well-known [3] the method of variation of parameters is a very useful tool in studying the properties of solutions of perturbed differential equations. Extending the classical variation of constants formula for linear systems, Alekseev [1] obtained a variation of constants formula for nonlinear systems. In [2], Lakshmikantham developed a nonlinear variation of constants formula for a scalar differential equation whose unperturbed term is of variable separable type, under rather mild assumptions. In this paper, we wish to study the general problem under weaker assumptions. Our approach is parallel to the classical one and yields two different formulas, one …

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Maximal And Minimal Solutions And Comparison Results For Differential Equations In Abstract Cones, V. Lakshmikantham, Roger W. Mitchell, A. Richard Mitchell Apr 1974

Maximal And Minimal Solutions And Comparison Results For Differential Equations In Abstract Cones, V. Lakshmikantham, Roger W. Mitchell, A. Richard Mitchell

Mathematics Technical Papers - Archive

As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by means of the extremal solutions of the corresponding differential equation. This comparison principle has been widely employed in studying the qualitative theory of differential equations (see [3]). If we desire to develop a similar comparison result in abstract spaces we must consider cones. These results could be of great value in applications to the theory of differential equations in abstract spaces. First, we must consider existence results for maximal and minimal solutions in cones which can …

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Lyapunov-Like Vector Functions Using Pointwise Degenerate Systems As Comparison Functions, Bernard A. Asner, V. Lakshmikantham Apr 1974

Lyapunov-Like Vector Functions Using Pointwise Degenerate Systems As Comparison Functions, Bernard A. Asner, V. Lakshmikantham

Mathematics Technical Papers - Archive

The use of Lyapunov-like vector functions is recognized as an important tool for estimating the behavior of a dynamical system. In applications, one needs to determine a suitable comparison function which contains information or properties that can be used to obtain some information about the behavior of the dynamical system. In recent years, the remarkable property of pointwise degeneracy has been discovered for linear, autonomous, delay-differential equations. For this class of equations one knows that all solutions will reach a subspace in finite time and remain on the subspace thereafter. As this class of equations is particularly simple, it becomes …

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Comparison Principle And Non Linear Contract In Abstract Spaces, V. Lakshmikantham, Jerome Eisenfeld Oct 1973

Comparison Principle And Non Linear Contract In Abstract Spaces, V. Lakshmikantham, Jerome Eisenfeld

Mathematics Technical Papers - Archive

The theory of differential and integral equations exploits comparison and iterative techniques which do not fall under the Contractive Mapping Principle. For they make use of partial orderings and maximal solutions; concepts which have no significance in a metric space. These methods take their proper place in the theory of cones [1], [2]. In this paper, Banach's Contraction Mapping Principle and comparison and iterative methods are brought together under a single roof which houses various results from the theory of differential equations [3], in addition to an interesting generalization of Banach's Theorem [4]. One 'It thus led, in a natural …

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The Existence Theorem Of Ordinary Differential Equations, Harris J. Dark Apr 1940

The Existence Theorem Of Ordinary Differential Equations, Harris J. Dark

Master's Theses

There are a great many devices for solving differential equations of certain special forms. But there is a large number of classes of differential equations that are not included in these special forms and cannot be integrated by quadratures or other purely elementary methods. When mathematicians were forced to abandon their cherished hope of finding a method for expressing the solution of every differential equation in terms of a finite number of known functions or their integrals they turned their attention to the question of whether a differential equation in general had a solution at all, and, if so, of …

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