A terminal comparison principle for differential inequalities

A Terminal Comparison Principle for Differential Inequalities

A Liouville comparison principle for solutions of quasilinear differential inequalities

This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form A(u) + |u|q−1u ≤ A(v) + |v|q−1v on Rn, where n ≥ 1, q > 0, and the operator A(w) belongs to a class of the so-called α-monotone operators. Typical examples of such operators are the p-Laplacian and its well-known modifications for 1 < p ≤ 2. The re...

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...

A Strong Maximum Principle for Quasilinear Parabolic Differential Inequalities

A maximum principle for C1 solutions of quasilinear parabolic differential inequalities which retains the strong conclusion of Nirenberg's well-known result [2] is established. The case of strongly differentiable solutions rather than of class C1 is also discussed.

A Comparison Principle for Terminal Value Problems in Ordinary Differential Equations

A comparison principle for a terminal value problem of an ordinary differential equation is formulated. Basic related topics such as the existence of maximal and minimal solutions of terminal value problems are investigated. The close relationship between the existence of the extremal solutions of a terminal value problem and the concept of asymptotic equilibrium of the differential equation is...