Differential inequalities and local valency

Random differential inequalities and comparison principles for nonlinear hybrid random differential equations

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

Fuzzy Local Fractional Differential Equations

Notes on Differential Equations and Differential Inequalities

The following Lemma gives conditions for the existence of a solution of a differential equation which is bounded on the domain R. Lemma 1.1. Given real numbers a < b, if f : (a, b) → R is a continuous, nonvanishing function, and there are some constants C1 > 0, C2 > 0, δ1 ∈ (0, b − a), δ2 ∈ (0, b − a) so that |f(t)| ≤ C1(t − a) for a < t < a + δ1 and |f(t)| ≤ C2(b − t) for b − δ2 < t < b, then ...

Differential variational inequalities

This paper introduces and studies the class of differential variational inequalities (DVIs) in a finite-dimensional Euclidean space. The DVI provides a powerful modeling paradigm for many applied problems in which dynamics, inequalities, and discontinuities are present; examples of such problems include constrained time-dependent physical systems with unilateral constraints, differential Nash g...

Two Local Inequalities

We assume that all varieties are projective, normal, and defined over C.