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, Schrdinger 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.
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.
"Many, often difficult and advanced, examples included into the text form an excellent review of a frontline of actual research in the area. ... In conclusion, the reviewer may recommend the book of Zou and Schechter as an excellent reference for those seeking new as well as well-established techniques in the critical point theory approach to differential equations." -Zentralblatt Math "In many variational problems, the functional Phi is strongly indefinite and does not satisfy the Palais-Smale condition. In this book, the authors present some of the latest work which has been done to overcome these difficulties and prove the existence of critical points. They also show how the abstract results can be applied to many problems in ordinary and partial differential equations." -Mathematical Reviews