The existence of solutions to classical variational problems without assuming convexity
نویسندگان
چکیده
منابع مشابه
Strict Convexity, Comparison Results and Existence of Solutions to Variational Problems
The aim of this paper is to discuss the assumption of strict convexity in problems of the the Calculus of Variations, and to present some results that avoid introducing this assumption. Mathematics Subject Classification (2000). Primary 49K20.
متن کاملExistence of Smooth Solutions to the Classical Moment Problems
Let s(0), s(l), ... be a given sequence, and define s(n) = s(—n) for n < 0 . If 2~Z I] íníms(m ~ n) t 0 holds for all finite sequences (in)nez . then it is known that there is a positive Borel measure p. on the circle T such that s(n) = f*n e"" dß(t), and conversely. Our main theorem provides a necessary and sufficient condition on the sequence (s(n)) that the measure p. may be chosen to be smo...
متن کاملA VARIATIONAL APPROACH TO THE EXISTENCE OF INFINITELY MANY SOLUTIONS FOR DIFFERENCE EQUATIONS
The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...
متن کاملExistence and Uniform Boundedness of Optimal Solutions of Variational Problems
Given an x0 ∈ Rn we study the infinite horizon problem of minimizing the expression ∫ T 0 f(t, x(t), x ′(t))dt as T grows to infinity where x : [0,∞) → Rn satisfies the initial condition x(0) = x0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0. We also establish that for every bounded set E ⊂ Rn the C([0, T ]) norms of approximate sol...
متن کاملNumerical Approach to the Estimation of Solutions of some Variational Problems with Convexity Constraints ∗
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection problems within a Principal-Agent framework. Problems such as product lines design, optimal taxation, structured derivatives design, etc. can be studied through th...
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: 1972
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1972-12913-6