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Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.
Riccati Differential Equations
In this paper we present a systematical approach to nonoscillation and disconjugacy normconditionn for linear differential systems and equations. We show that the infima of the appropriate integral functionals are constants for nonoscillation and disconjugacy criteria. Applying an interative method we prove that for some variational problems the minimal solutions exist and satisfy the Euler-Lagrange equations. We compute the infima in questions in certain cases. Thus we obtain many known and new nonoscillation and disconjugacy criteria. Finally, we apply our results to establish uniqueness of multipoint boundary value problems for certain nonlinear systems and equations.

Technical Note

University of Maryland, College Park. Institute for Fluid Dynamics and Applied Mathematics

Published: 1965

Total Pages: 276


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AFOSR.

United States. Air Force. Office of Scientific Research

Published: 1950

Total Pages: 1190


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