Approximation of eigenvalues of differential equations with non-smooth coefficients
Approximation of isolated eigenvalues of ordinary differential operators.
Approximation von Eigenwertproblemen bei nichtlinearer Parameterabhängigkeit.
Asymmetric bound states of differential equations in nonlinear optics
Asymptotic analysis of non-self-adjoint Hill operators
We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator...
Asymptotic behaviour of the solutions of equations with impulse effect in a Banach space.
Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.
Asymptotic normality of eigenvalues of random ordinary differential operators
Boundary value problems for ordinary differential equations with random coefficients are dealt with. The coefficients are assumed to be Gaussian vectorial stationary processes multiplied by intensity functions and converging to the white noise process. A theorem on the limit distribution of the random eigenvalues is presented together with applications in mechanics and dynamics.
Asymptotics of eigensections on toric varieties
Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities for eigensections approaching a semiclassical ray. Here is a normal compact toric variety and is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch....
Asymptotics of the number of zeros and of the eigenvalues of general weighted Sturm-Liouville problems.
Asymptotique semi-classique pour la densité spectrale locale d'opérateurs de Schrödinger (d'après D. Robert et H. Tamura)
Asypmtotic formulas of eigenvalues and eigenfucntions on non-autonomous semilinear Sturm-Liouville problems.