scispace - formally typeset
Journal ArticleDOI

Topological methods in the theory of nonlinear integral equations

M. A. Krasnoselʹskii
- 01 Mar 1968 - 
- Vol. 75, Iss: 3, pp 318
Reads0
Chats0
About
This article is published in American Mathematical Monthly.The article was published on 1968-03-01. It has received 1859 citations till now. The article focuses on the topics: Integral equation & Summation equation.

read more

Citations
More filters
Journal ArticleDOI

Dual variational methods in critical point theory and applications

TL;DR: In this paper, general existence theorems for critical points of a continuously differentiable functional I on a real Banach space are given for the case in which I is even.
Book

Minimax methods in critical point theory with applications to differential equations

TL;DR: The mountain pass theorem and its application in Hamiltonian systems can be found in this paper, where the saddle point theorem is extended to the case of symmetric functionals with symmetries and index theorems.
Journal ArticleDOI

On the nature of turbulence

TL;DR: A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed in this article, where the authors propose a mechanism for generating turbulence in a dissipative system with respect to dissipative energy.
Journal ArticleDOI

On the variational principle

TL;DR: The variational principle states that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every E > 0, there exists some point u( where 11 F'(uJj* < l, i.e., its derivative can be made arbitrarily small as discussed by the authors.
Journal ArticleDOI

Some global results for nonlinear eigenvalue problems

TL;DR: In this paper, the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space is investigated, and the existence of continua, i.e., closed connected sets, of solutions of these equations is demonstrated.