Browsing Technical Papers - DO NOT EDIT by Author "Mitchell, A. Richard"
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Asymptotic Equilibrium of Ordinary Differential Systems in a Banach Space
Mitchell, Roger W.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1974-03)**Please note that the full text is embargoed** ABSTRACT: A differential system [see pdf for notation] where [see pdf for notation] has asymptotic equilibrium if 1) for any initial condition [see pdf for notation] the ... -
Existence of Solutions of Boundary Value Problems for Nonlinear Second Order Systems in a Banach Space
Mitchell, A. Richard; Chandra, V. (University of Texas at ArlingtonDepartment of Mathematics, 1977-03)**Please note that the full text is embargoed** ABSTRACT: This paper is concerned with the existence of solutions of boundary value problems (BVP, for short) for nonlinear second order ordinary differential equations of ... -
Maximal and Minimal Solutions and Comparison Principle for Differential Equations in Abstract Cones
Mitchell, Roger W.; Mitchell, A. Richard; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)**Please note that the full text is embargoed** ABSTRACT: Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result ... -
Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones
Lakshmikantham, V.; Mitchell, Roger W.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1974-04)**Please note that the full text is embargoed** ABSTRACT: As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by ... -
The Method of Quasilinearization and Positivity of Solutions in Abstract Cones
Lakshmikantham, V.; Sety, Dolores D.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1976-03)**Please note that the full text is embargoed** ABSTRACT: The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the ... -
A New Approach to the Method of Nonlinear Variation of Parameters
Mitchell, A. Richard; Lord, M. E. (University of Texas at ArlingtonDepartment of Mathematics, 1975-01)**Please note that the full text is embargoed** ABSTRACT: 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 ... -
On the Existence of Solutions of Differential Equations and Zeros of Operators in K-Banach Spaces
Bronson, Evin; Tennison, R. L.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1975)**Please note that the full text is embargoed** ABSTRACT: 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 ... -
On the Existence of Solutions of Differential Equations of Retarded Type in a Banach Space
Lakshmikantham, V.; Mitchell, Roger W.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)**Please note that the full text is embargoed** ABSTRACT: The existence and uniqueness of solutions of differential equations of retarded type in a Banach space are considered under a monotonicity type condition. The tools ... -
On the Existence of Weak Solutions of Differential Equations in Nonreflexive Banach Spaces
Lakshmikantham, V.; Bronson, Evin; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1977-03)**Please note that the full text is embargoed** ABSTRACT: The study of the Cauchy problem for differential equations in a Banach space relative to the strong topology has attracted much attention in recent years [2,4,5,7]. ...