Journal ArticleDOI
Nonlinear mapping theory and the continuation of solutions of equations under homotopy
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This article is published in Nonlinear Analysis-theory Methods & Applications.The article was published on 1980-01-02. It has received 0 citations till now. The article focuses on the topics: Homotopy analysis method & n-connected.read more
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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.
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Fixed point theorems for mappings satisfying inwardness conditions
TL;DR: In this paper, a characterization of weakly inward mappings is given in terms of a condition arising in the study of ordinary differential equations, and a general fixed point theorem is proved and applied to derive a generalization of the contraction mapping principle in a complete metric space.
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A general principle on ordered sets in nonlinear functional analysis
Haim Brezis,Felix E. Browder +1 more
TL;DR: In this paper, a general and very simple principle concerning order relations is proposed to unify a number of diverse results in nonlinear functional analysis, such as the normal solvability theorems, generalizations of the Bishop-Phelps theorem, invariance theorem for closed sets under flows in metric spaces, and a number other new related results.