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Sufficient conditions for the $n$ -th order linear differential equation are derived which guarantee that its Cauchy function $K$ , together with its derivatives $\frac{\partial^{i} K}{\partial t^{i}}$ , $i = 1, \dots, n - 1$ , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.

Some compactness methods in the theory of nonlinear evolution equations with applications to P.D.E.

Ioan I. Vrabie (1987)

Banach Center Publications

Some comparisons of difference schemes on meshes of Shishkin and Bakhvalov type.

Surla, Katarina, Herceg, Dragoslav, Maličić, Helena (2001)

Novi Sad Journal of Mathematics

Some converse theorems in the asymptotic theory of ordinary differential equations

Jaromír Šimša (1988)

Czechoslovak Mathematical Journal

Some differential equations with delay

Corduneanu, C. (1973)

Proceedings of Equadiff III

Some dynamic inequalities applicable to partial integrodifferential equations on time scales

Deepak B. Pachpatte (2015)

Archivum Mathematicum

The main objective of the paper is to study explicit bounds of certain dynamic integral inequalities on time scales. Using these inequalities we prove the uniqueness of some partial integrodifferential equations on time scales.

Some estimates for the first eigenvalue of the Sturm-Liouville problem with a weight integral condition

Maria Telnova (2012)

Mathematica Bohemica

Let $λ_{1} (Q)$ be the first eigenvalue of the Sturm-Liouville problem $y^{''} - Q (x) y + λ y = 0, y (0) = y (1) = 0, 0 < x < 1 .$ We give some estimates for $m_{α, β, γ} = {inf}_{Q \in T_{α, β, γ}} λ_{1} (Q)$ and $M_{α, β, γ} = {sup}_{Q \in T_{α, β, γ}} λ_{1} (Q)$ , where $T_{α, β, γ}$ is the set of real-valued measurable on $[0, 1]$ $x^{α} ...$

Some estimates for the minimal eigenvalue of the Sturm-Liouville problem with third-type boundary conditions

Elena Karulina (2011) Mathematica Bohemica

We consider the Sturm-Liouville problem with symmetric boundary conditions and an integral condition. We estimate the first eigenvalue

λ_{1}

of this problem for different values of the parameters.

Some examples for the extended use of the parametric representation method

Simon, Peter L., Farkas, Henrik (1998)

Proceedings of Equadiff 9

Some examples for the Poincaré and Painlevé problems

Alcides Lins Neto (2002)

Annales scientifiques de l'École Normale Supérieure

Some Examples of Rigid Representations

Kostov, Vladimir (2000)

Serdica Mathematical Journal

*Research partially supported by INTAS grant 97-1644.Consider the Deligne-Simpson problem: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) (resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matrices Mj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp. A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromy operators and as matrices-residua of fuchsian systems on Riemann’s sphere. We give new examples...

Some existence and bifurcation results for solutions of nonlinear Sturm-Liouville eigenvalue problems.

Chao-Nien Chen (1991)

Mathematische Zeitschrift

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