Necessary and sufficient conditions for a system of eigenfunctions and associated functions of a Sturm-Liouville operator with discontinuous coefficients to possess the basis property.
New method for computation of discrete spectrum of radical Schrödinger operator
A new method for computation of eigenvalues of the radial Schrödinger operator is presented. The potential is assumed to behave as if and as if . The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function . It is shown that the eigenvalues are the discontinuity points of the function . Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison...
New polynomials for which has a solution with almost all real zeros.
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
Nichtselbstadjungierte Differentialoperatoren im nichtkompakten Fall.
Nicht-S-hermitesche Rand- und Eigenwertprobleme.
Nodal solutions for a second-order -point boundary value problem
We study the existence of nodal solutions of the -point boundary value problem where
Nodes of eigenfunctions of a certain class of ordinary differential equations of the fourth order
Nonclassical Sturm-Liouville problems and Schrödinger operators on radial trees.
Nonhermitian systems and pseudospectra
Four applications are outlined of pseudospectra of highly nonnormal linear operators.
Nonlinear discrete periodic boundary value problems at resonance.
Nonlinear eigenvalue problems for fourth order ordinary differential equations
This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of...
Nonlinear elliptic boundary value problems versus their finite difference approximations: numerically irrelevant solutions.
Nonlinear Extensions of Limit-Point Criteria.
Nonlinear functional Sturm-Liouville equations
Nonlinear systems with mean curvature-like operators
We give an existence result for a periodic boundary value problem involving mean curvature-like operators. Following a recent work of R. Manásevich and J. Mawhin, we use an approach based on the Leray-Schauder degree.
Non-self-adjoint singular Sturm-Liouville problems with boundary conditions dependent on the eigenparameter.
Note on a paper of E. M. E. Zayed and S. F. M. Ibraham.
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number k of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large k are large nonlinear exponents σ. In a second part, we compute...