Inequalities of critical point theory
نویسندگان
چکیده
منابع مشابه
Inequalities of Critical Point Theory
A purpose of critical point theory is the counting of critical points of functions. Principal theorems in the subject state in precise terms that topological complexity of the underlying space is reflected in the existence and nature of critical points of any smooth real-valued function defined on the space. The initial development of critical point theory is peculiarly the work of one man, Mar...
متن کاملLecture 38: Applications of Critical Point Theory
1. Generalized Sphere Theorem As a first application of the critical point theory of distance funciton, we shall prove Theorem 1.1 (Grove-Shiohama). Let (M, g) be a complete simply connected Riemann-ian manifold with K > 1 4 and diam(M, g) ≥ π, then M is homeomorphic to S m. So Grove-Shiohama's theorem implies the sphere theorem. Proof. Let p, q ∈ M so that dist(p, q) = diam(M, g). In what foll...
متن کاملSolvability of an impulsive boundary value problem on the half-line via critical point theory
In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.
متن کاملJean Mawhin’s contributions to critical point theory
Content The first paper by Jean Mawhin on critical point theory [] was published in and was devoted to periodic solutions of a forced pendulum equation. One of the most recent papers in [] concerns periodic solutions of difference systems with φ-Laplacian. It is impossible to describe all the contributions. We have selected articles, books and some fundamental topics: the force...
متن کاملQuantitative Deformation Theorems and Critical Point Theory
It is well known that deformation theorems are the basic tools in critical point theory. They can be derived under a condition of Palais-Smale type ((PS), for short). In the classical setting of a C1 functional f defined on a Banach space X (or a C2 Finsler manifold), we refer to [15]; for a continuous functional f defined on a complete metric space X, we refer to [8], the results of which incl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1958
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1958-10137-8