Comparison theorems for elliptic differential systems

Comparison Theorems for Special Classes of Nonselfadjoint Elliptic Equations

Known comparisons for nonselfadjoint elliptic equations are strengthened in cases where the coefficients of these equations satisfy special conditions. These improved comparison theorems are also considered in the context of a related eigenvalue problem.

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Comparison Theorems for Fourth Order Differential Equations Garret

This paper establishes an apparently overlooked relationship between the iv yiV p'air of fourth order line,r equations y p(x)y 0 and + p(x)y 0, where p is , positive, continuous function defined on [O,m). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equatio...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

On Comparison Theorems for Conformable Fractional Differential Equations

In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm’s separation and Sturm’s comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented t...