Playing Around Resonance

“Fonda’s Playing Around Resonance focuses on the material needed to develop research in ‘the existence of solutions’ to a type of nonlinear boundary value problem. In particular, he concentrates on providing the theory to research periodic solutions to second order ordinary differential equations. … it is truly geared more toward graduate students. Summing Up: Recommended. Graduate students, researchers, and faculty.” (S. L. Sullivan, Choice, Vol. 54 (11), July, 2017)“This is an excellent book, well organized and full of well-explained results and techniques on the subject. The proofs of the theorems are rigorous and well written, the arguments are presented in a clear and pleasurable way. The final section of each chapter … provides information useful to a better understanding of the history of the results contained in the book. … used as a textbook in an advanced course dealing with periodic solutions for second-order ordinary differential equations.” (Addolorata Salvatore, Mathematical Reviews, 2017)

• 1.Preliminaries on Hilbert spaces.- 2.Operators in Hilbert spaces.- 3.The semilinear problem.- 4.The topological degree.- 5.Nonresonance and topological degree.- 6.Playing around resonance.- 7.The variational method.- 8.At resonance, again.- 9.Lusternik-Schnirelmann theory. 10.The Poincaré-Birkhoff theorem.- 11.A myriad of periodic solutions.