By Wenming Zou
This e-book provides many of the most up-to-date study in severe aspect concept, describing tools and featuring the latest functions. assurance contains extrema, even valued functionals, susceptible and double linking, signal altering options, Morse inequalities, and cohomology teams. functions defined contain Hamiltonian structures, Schrödinger equations and structures, leaping nonlinearities, elliptic equations and platforms, superlinear difficulties and beam equations.
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Extra resources for Critical Point Theory and Its Applications
This completes the proof D Notes and Comments. 2 are known as fountain theorems since the critical points spout out like a fountain. The earlier form of the fountain theorem and its dual were established by T. Bartsch in  and by T. Bartsch-M. Willem in  (see also T. Bartsch-M. Willem [49, 50] and M. Willem  ) respectively, where the (PS) condition and its variants play an important role for those abstract results and their applications. They are effective tools in studying the existence of infinitely many large or small energy solutions.
Possibly, it can be proved by other methods such as the degree theory or the contraction mapping principle. 4 has far more extended applications. We would like to leave them to the readers. Chapter 3 Even Functionals In this chapter we present some abstract theorems which concern the existence of infinitely many critical points for even functionals. The Palais-Smale type compactness condition is not necessary for the new results. By taking advantage of the abstract theorems, we study the existence of infinitely many large energy solutions for nonlinear Schrodinger equations and of infinitely many small energy solutions for semilinear elliptic equations with concave and convex nonlinear it ies.
6. D Notes and Comments. g. A. Ambrosetti-P. Rabinowitz ). The readers may find some variants of it in M. Struwe . 3. SMALL ENERGY SOLUTIONS 49 high energy solutions via SMP and the Fountain Theorem (cf. P. Rabinowitz , T. Bartsch , T. Bartsch-M. Wihem , M. Struwe , and also M. Willem , etc). In particular, in T. Bartsch-Z. Liu-T. Weth , S. Li-Z. Q. Wang  and W. Zou , sign-changing high energy solutions were obtained. We will address this topic later in this book.