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Topological methods in the theory of nonlinear integral equations
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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
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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.
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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
David Ruelle,Floris Takens +1 more
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.
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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.