摘要:

The present paper deals with the problem of constructing and proving asymptotic expansions for nonlinear, singularly perturbed difference equations. New methods for the construction of asymptotic expansions are presented and compared with well-known ones. For the proof of their validity, fundamental principles for the treatment of nonlinear singular perturbation problems are applied, based on the concepts of e-stability, formal asymptotic expansions, matching and asymptotic expansions. The results are derived from a general theory of asymptotic expansions of nonlinear operator equations that has been developed recently by the author.

ISSN:0163-0563    

DOI:10.1080/01630567908816035

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

This paper is concerned with the approximate solution of nonlinear operator equations in abstract settings and with applications to integral and differential equations. A given operator with certain continuity and compactness or inverse compactness properties is a suitable limit of a sequence of operators with analogous properties which hold uniformly or asymptotically. Both fixed point equations and inhomogeneous equations are treated. Solutions of approximate problems converge to solutions of the given problem. This is an appropriate type of set convergence when solutions are not unique.

ISSN:0163-0563    

DOI:10.1080/01630567908816036

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630567908816037

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

We consider a semicoercive variational inequality (V) (see def. below) under nonlinear mixed boundary conditions: u≥o on r1and u≤o on r2. Here r1and r2are the basic components of the boundary ∂Ω of a bounded domain Ω ⊂ ℝ2. Problem (V) corresponds to a boundary value problem for the Poisson equation Δu=f in Ω, as well as to a convex minimization problem (M). We study the questions of existence, uniqueness and regularity of the solutions to this problem. One of the tools involved is a penalty method which could also be interpreted as a singular perturbation or Yosida-approximation technique. The paper extends the results of [9] to noncoercive boundary conditions.

ISSN:0163-0563    

DOI:10.1080/01630567908816038

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

An application of the method of contractor directions to nonlinear programming in Banach spaces is presented. The main objective is to show that milder conditions can be imposed on nonlinear equality constraints. A generalization of Lusternik's theorem is included.

ISSN:0163-0563    

DOI:10.1080/01630567908816039

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

A direct treatement of a nonlinear operator equation arising in control theory is given.

ISSN:0163-0563    

DOI:10.1080/01630567908816040

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630567908816034

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor