Let X be a Finsler manifold. We prove some abstract results on the existence of critical points for strongly indefinite functionals f ∈ C1(X ,R) via a new deformation theorem. Different from the works in the literature, the new deformation theorem is constructed under a new version of Cerami-type condition instead of Palais-Smale condition. As applications, we prove the existence of multiple pe...

In this article we study the existence of critical points for certain superquadratic strongly indefinite even functionals appearing in the study of periodic solutions of Hamiltonian systems and solutions of certain class of Elliptic Systems. We first present two abstract critical point theorems for even functionals. These results are well suited for our applications, but they are interesting by...

Optimal Ergodic Control of Linear Stochastic Differential Equations with Quadratic Cost Functionals Having Indefinite Weights

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

Take a C function f :M → R on a complete Hilbert manifold which satisfies the Palais–Smale condition. Assume that it is a Morse function, meaning that the second order differential df(x) is non-degenerate at every critical point x. Recall that the Morse index m(x, f) of a critical point x is the dimension of the maximal subspace on which df(x) is negative definite. Then the basic result of Mors...

Let X be a real Banach space and let K be a bounded closed convex subset of X. We prove that the set of strongly exposing functions K" of K is a (norm) dense G, in X* if and only if for any bounded closed convex subset C such that Kit C, there exists a point x in K which is a strongly exposed point of conv (C U K). As an application, we show that if X* is weakly compact generated, then for any ...