Boundary problems of the second order with an indefinite weight-function.
Boundary value problems for nonlinear perturbations of some ϕ-Laplacians
This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form (ϕ(u'))' = f(t,u,u') submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space, to which Leray-Schauder...
Boundary value problems with jumping nonlinearities
Boundary value problems with regular singularities and singular boundary conditions.
Boundary-value problems for ordinary differential equations with matrix coefficients containing a spectral parameter.
Branch Switching in Bifurcation Problems for Ordinary Differential Equations
C*-Algebras of Singular Integral operators on the line realted to singular Sturm-Liouville problems.
Calogero-Moser spaces and an adelic -algebra
We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.
Characterizing degenerate Sturm-Liouville problems.
Chord Techniques and Newton's Method for Discrete Bifurcation Problems.
Coefficients de réflexion pour les potentiels de Hardy
Compactness of the inverse of the minimal operator for a class of ordinary differential expressions.
Comparison between the variational iteration method and the homotopy perturbation method for the Sturm-Liouville differential equation.
Comparison of eigenvalues for a fourth-order four-point boundary value problem.
Computing eigenvalues of regular Sturm-Liouville problems.
Connected branches of asymptotically equivalent solutions to non-linear eigenvalue problems
We prove an existence theorem for connected branches of solutions to nonlinear operator equations in Banach spaces. This abstract result is applied to the asymptotically equivalent solutions to nonlinear ordinary differential equations.
Continuous Branches of Positive Solutions for a Class of Nonlinear Second-Order Differential Equations.
Controlling nonuniqueness of local invariant manifolds.
Convergence of eigenfunction expansions corresponding to nonlinear Sturm-Liouville operators.
Convolution algebras arising from Sturm-Liouville transforms and applications.