EuDML | Browse

The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient $λ^{2} q (s), s \in [s_{0}, \infty)$ is investigated, where $λ \in ℝ$ and $q (s)$ is a nondecreasing step function tending to $\infty$ as $s \to \infty$ . Let $S$ denote the set of those $λ$ ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that $S$ is an additive group. Four examples are given with $S = {0}$ , $S = ℤ$ , $S = 𝔻$ (i.e. the set of dyadic numbers), and $ℚ \subset S ⫋ ℝ$ .

Adiabatic theory : stability of systems with increasing gaps

G. Nenciu (1997)

Annales de l'I.H.P. Physique théorique

Adjoint and self-adjoint differential operators on graphs.

Carlson, Robert (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions

H. Frankowska (1985)

Annales de l'I.H.P. Analyse non linéaire

Adjoint domains and generalized splines

Richard C. Brown (1975)

Czechoslovak Mathematical Journal

Adjoint operators and boundary value problems for linear differential equations

Mihály Pituk (1991)

Mathematica Slovaca

Adjoints of solution semigroups and identifiability of delay differential equations in Hilbert spaces.

Mastinšek, M. (1994)

Acta Mathematica Universitatis Comenianae. New Series

Adjungierte und selbstadjungierte lineare Differentialgleichungen

Zdeněk Hustý (1965)

Archivum Mathematicum

Admissible spaces for a first order differential equation with delayed argument

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster (2019)

Czechoslovak Mathematical Journal

We consider the equation $- y^{'} (x) + q (x) y (x - ϕ (x)) = f (x), x \in ℝ,$ where $ϕ$ and $q$ ( $q \geq 1$ ) are positive continuous functions for all $x \in ℝ$ and $f \in C (ℝ)$ . By a solution of the equation we mean any function $y$ , continuously differentiable everywhere in $ℝ$ , which satisfies the equation for all $x \in ℝ$ . We show that under certain additional conditions on the functions $ϕ$ and $q$ , the above equation has a unique solution $y$ , satisfying the inequality $∥ y^{'} ∥_{C (ℝ)} + {∥ q y ∥}_{C (ℝ)} \leq c {∥ f ∥}_{C (ℝ)},$ where the constant $c \in (0, \infty)$ does not depend on the choice of $f$ .

Currently displaying 601 – 620 of 1233

Previous Page 31 Next