Nontrivial critical points for asymptotically quadratic function

Existence of Multiple Critical Points for an Asymptotically Quadratic Functional with Applications

Morse theory for isolated critical points at infinity is used for the existence of multiple critical points for an asymptotically quadratic functional. Applications are also given for the existence of multiple nontrivial periodic solutions of asymptotically Hamiltonian systems.

Nontrivial Solutions for Asymptotically Linear Variational Inequalities

The aim of this paper is to extend to variational inequalities a result of Amann and Zehnder’s, refined by Chang (see [1, 6, 14]), concerning the existence of nontrivial solutions for a semilinear elliptic boundary value problem, when the nonlinearity is asymptotically linear, is zero at zero and its derivative has a suitable jump between zero and infinity. In the constrained problem studied he...

Monodromy problem for the degenerate critical points

For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...

The Critical Points of a Function

Nontrivial asymptotically nonfree gauge theories and dynamical unification of couplings.

An evidence for nontriviality of asymptotically non-free (ANF) Yang-Mills theories is found on the basis of optimized perturbation theory. It is argued that these theories with matter couplings can be made nontrivial by means of the reduction of couplings, leading to the idea of dynamical unification of couplings (DUC) The second-order reduction of couplings in the ANF SU(3)-gauged Higgs-Yukawa...