Bethe ansatz solutions to quasi exactly solvable difference equations.
Beurling vectors of quasielliptic systems of differential operators.
Beyond the classical Weyl and Colin de Verdière’s formulas for Schrödinger operators with polynomial magnetic and electric fields
We present a pair of conjectural formulas that compute the leading term of the spectral asymptotics of a Schrödinger operator on with quasi-homogeneous polynomial magnetic and electric fields. The construction is based on the orbit method due to Kirillov. It makes sense for any nilpotent Lie algebra and is related to the geometry of coadjoint orbits, as well as to the growth properties of certain “algebraic integrals,” studied by Nilsson. By using the direct variational method, we prove that the...
B-Functions and Holonomic Systems. Rationality of Roots of B-Functions
Bifurcating solutions to the monodomain model equipped with FitzHugh-Nagumo kinetics.
Bifurcation analysis of stimulated Brillouin scattering
Bifurcation and multiplicity results for a nonhomogeneous semilinear elliptic problem.
Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
Bifurcation and symmetry in problems of capillary-gravity waves.
Bifurcation de Hopf d’ondes de choc pour les équations de Navier-Stokes compressible
Bifurcation for a semilinear elliptic equation on Rn with radially symmetric coefficients.
Bifurcation for Monge-Ampère Equations on Flat Tori.
Bifurcation for nonlinear elliptic boundary value problems I.
This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the...
Bifurcation for odd nonlinear elliptic variational inequalities
Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
Bifurcation from the spectrum towards regular values.
Bifurcation in mathematical models of social and economic interaction
Bifurcation in the solution set of the von Kármán equations of an elastic disk lying on an elastic foundation
We investigate bifurcation in the solution set of the von Kármán equations on a disk Ω ⊂ ℝ² with two positive parameters α and β. The equations describe the behaviour of an elastic thin round plate lying on an elastic base under the action of a compressing force. The method of analysis is based on reducing the problem to an operator equation in real Banach spaces with a nonlinear Fredholm map F of index zero (to be defined later) that depends on the parameters α and β. Applying the implicit function...
Bifurcation of free vibrations for completely resonant wave equations
We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.
Bifurcation of nonlinear elliptic system from the first eigenvalue.