Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

1. Front Matter

   Pages i-xi

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2. Sobolev Spaces

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 1-13

3. Nonlinear Operators

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 15-44

4. Nonsmooth Analysis

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 45-59

5. Degree Theory

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 61-96

6. Variational Principles and Critical Point Theory

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 97-139

7. Morse Theory

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 141-179

8. Bifurcation Theory

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 181-200

9. Regularity Theorems and Maximum Principles

   • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

   Pages 201-222

10. Spectrum of Differential Operators

    • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

    Pages 223-270

11. Ordinary Differential Equations

    • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

    Pages 271-302

12. Nonlinear Elliptic Equations with Dirichlet Boundary Conditions

    • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

    Pages 303-385

13. Nonlinear Elliptic Equations with Neumann Boundary Conditions

    • Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou

    Pages 387-436

14. Back Matter

    Pages 437-459

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This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.

• Convex function
• Degree theory
• Minimization
• Morse theory
• Nonlinear operators
• Sobolev spaces
• partial differential equations
• ordinary differential equations

From the book reviews:

“This volume is devoted to the qualitative analysis of some basic classes of nonlinear boundary value problems by means of modern variational and topological methods. … This material appears here for the first time in book form. The presentation is very clear and an extensive bibliography (397 titles) and a rich index highlight the text. This work will serve as a reference for researchers working in pure and applied nonlinear analysis.” (Vicenţiu D. Rădulescu, zbMATH, 2014)

• Department of Mathematics, University of Perpignan, Perpignan, France

  Dumitru Motreanu

• Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel

  Viorica Venera Motreanu

• Department of Mathematics, National Technical University Zografou Campus, Athens, Greece

  Nikolaos Papageorgiou

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