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*Research partially supported by INTAS grant 97-1644.Consider the Deligne-Simpson problem: give necessary and
sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C)
(resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matrices
Mj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp.
A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromy
operators and as matrices-residua of fuchsian systems on Riemann’s sphere.
We give new examples...
Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.
In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.
We consider nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition. We investigate the structure of the set of bifurcation points, and study the behavior of two families of continua of nontrivial solutions of this problem contained in the classes of functions having oscillation properties of the eigenfunctions of the corresponding linear problem, and bifurcating from the points and intervals of the line of trivial solutions.
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