Third Order Linear Differential Equations, Softcover reprint of the original 1st ed. 1987 Coll. Mathematics and its Applications, Vol. 22

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Gad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. How­ ever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the stI11fture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisci­ plines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifi~ation schemes.

I. Third Order Linear Homogeneous Differential Equations in Normal Form.- §1. Fundamental Properties of Solutions of the Third Order Linear Homogeneous Differential Equation.- §2. Oscillatory Properties of Solutions of the Differential Equation (a).- §3. Asymptotic Properties of Solutions of the Differential Equations (a) and (b).- §4. Boundary Value Problems.- II. Third Order Linear Homogeneous Differential Equations with Continuous Coefficients.- §5. Principal Properties of Solutions of Linear Homogeneous Third Order Differential Equations with Continuous Coefficients.- §6. Conditions for Disconjugateness, Non-oscillatoricity and Oscillatoricity of Solutions of the Differential Equation (A).- §7. Comparison Theorems for Differential Equations of Type (A) and Their Applications.- III. Concluding Remarks.- 1. Special Forms of Third Order Differential Equations.- 2. Remark on Mutual Transformation of Solutions of Third Order Differential Equations.- IV. Applications of Third Order Linear Differential Equation Theory.- §8. Some Applications of Linear Third Order Differential Equation Theory to Non-linear Third Order Problems.- §9. Physical and Engineering Applications of Third Order Differential Equations.- References.