## Exercises in Analysis: Part 2: Nonlinear AnalysisThis second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods. Each of five topics corresponds to a different chapter with inclusion of the basic theory and accompanying main definitions and results,followed by suitable comments and remarks for better understanding of the material. Exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume. |

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Exercises in Analysis: Part 2: Nonlinear Analysis Leszek Gasiński,Nikolaos S. Papageorgiou No preview available - 2016 |

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A(un Arguing by contradiction assume bounded open set bounded sets C C X conclude continuous map convergence convex function convex set critical point defined Definition denote dist(u dºs eaſists exists find a sequence finite dimensional finite measure space Fréchet differentiable Gâteaux differentiable H-co hence Hilbert space hypothesis implies inſ Lebesgue measure Let Q C R Let u e lim inf lim sup Lipschitz boundary Lipschitz continuous locally Lipschitz lower semicontinuous maximal monotone metric space nonempty norm open set p(un Proposition recall reflexive Banach space Remark s p(u satisfies the C-condition Show ſº Solution of Problem space and let subsequence if necessary subset T-lim theorem see Theorem To(X topological space uniformly upper semicontinuous weak topology weakly WºO z e Q