Manual Semilinear Elliptic Equations for Beginners: Existence Results via the Variational Approach

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Existence Results via the Variational Approach

Check system status. Toggle navigation Menu. Name of resource. Problem URL. Describe the connection issue. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Semilinear elliptic equations arise in a variety of contexts in geometry, physics, mechanics, engineering and, more recently, in life sciences.

None of these fields can be investigated without taking into account non- linear phenomena, and variational methods, as a branch or an evolution of the Cal- culus of Variations, are almost entirely concerned with nonlinearity. The theory has attained a spectacular success in the last thirty-or-so years, reaching a high level of complexity and refinement, and its applications are scattered throughout thousands of research papers.


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Furthermore, some of the simplest methods within the varia- tional approach are nowadays classical tools in the field of nonlinear differential equations as fixed point and monotonicity methods are. They have become, in other words, part of the toolbox that any researcher in the field is supposed to have at hand. This poses a stimulating problem: how to teach variational methods and semi- linear elliptic equations to upcoming generations of students. In our teaching ex- perience, we have noticed a recurrent phenomenon.

Up to a certain grade, students possess a rather general knowledge of basic principles, for instance in Functional Analysis. At the next step however they are often confronted with problems taken from real research. Richard Bellman. Current Topics in Summability Theory and Applications.

Hemen Dutta. Leonid Shaikhet. Fabio Botelho. Nonlinear Analysis. Qamrul Hasan Ansari. Rolando Magnanini. Angelo Favini. Lectures on Functional Analysis and the Lebesgue Integral.

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Vilmos Komornik. Geometries and Transformations. Norman W. Structure and Geometry of Lie Groups.

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