Details

Autor(en) / Beteiligte

• Chang, K. W.,
• Howes, Frederick A.,

Titel

Nonlinear singular pertubation phenomena : theory and applications

Auflage

1st ed. 1984

Ort / Verlag

New York : Springer Science+Business Media, LLC,

Erscheinungsjahr

[1984]

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• Bibliographic Level Mode of Issuance: Monograph
• Includes bibliographical references and index.
• I. Introduction -- II. A’priori Bounds and Existence Theorems -- III. Semilinear Singular Perturbation Problems -- IV. Quasilinear Singular Perturbation Problems -- V. Quadratic Singular Perturbation Problems -- VI. Superquadratic Singular Perturbation Problems -- VII. Singularly Perturbed Systems -- VIII. Examples and Applications -- References -- Author Index -- Sybject Index.
• Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the existence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly questions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary differential equations, by means of the consistent use of differential inequality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equations. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council.
• English
• Description based on print version record.