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Nonlinear Functional Analysis
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A survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis can be found in this article, with extensive commentary, many examples, and interesting, challenging exercises.Abstract:
This graduate-level text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting, challenging exercises. Topics include degree mappings for infinite dimensional spaces, the inverse function theory, the implicit function theory, Newton's methods, and many other subjects. 1985 edition.read more
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Differential equations with discontinuous right-hand sides☆
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Finite Volume Methods
TL;DR: The finite volume method is a discretization method that is well suited for the numerical simulation of various types (for instance, elliptic, parabolic, or hyperbolic) of conservation laws.
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Cone metric spaces and fixed point theorems of contractive mappings
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TL;DR: In this paper, the authors introduce cone metric spaces and prove fixed point theorems of contractive mappings on these spaces, and prove some fixed point properties of the mappings.
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Attractors for random dynamical systems
Hans Crauel,Franco Flandoli +1 more
TL;DR: In this article, a criterion for existence of global random attractors for RDS is established and the existence of invariant Markov measures supported by the random attractor is proved for SPDE, which yields invariant measures for the associated Markov semigroup.
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Analysis of bounded variation penalty methods for ill-posed problems
TL;DR: In this paper, an abstract analysis of bounded variation methods for ill-posed operator equations is presented, and convergence results are obtained when these perturbations vanish and the regularization parameter is chosen appropriately.