Critical Point Theory and Its Applications (eBook)

Wenming Zou, Martin Schechter (Autoren)

eBook Download: PDF

2006
XII, 318 Seiten
Springer US (Verlag)
978-0-387-32968-0 (ISBN)

Infos

This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.

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Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods. Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications. The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrodinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition.

Inhalt

Preliminaries.- Functionals Bounded Below.- Even Functionals.- Linking and Homoclinic Type Solutions.- Double Linking Theorems.- Superlinear Problems.- Systems with Hamiltonian Potentials.- Linking and Elliptic Systems.- Sign-Changing Solutions.- Cohomology Groups.

Produkt-Details

• Erscheint lt. Verlag: 10.9.2006
• Zusatzinfo: XII, 318 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• Schlagworte: Calculus • Cohomology group • Compactness • Extrema • Homoclinic orbits • Linking • Minimum • Ordinary differential equations • Partial differential equations • Schrödinger equations • Sign-changing solutions
• ISBN-10: 0-387-32968-4 / 0387329684
• ISBN-13: 978-0-387-32968-0 / 9780387329680