A maximum principle for nonlinear differential inequalities

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 Terminal Comparison Principle for Differential Inequalities

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 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...

The Maximum Principle for Viscosity Solutions of Fully Nonlinear Second Order Partial Differential Equations

We prove that viscosity solutions in W 1'~176 of the second order, fully nonlinear, equation F(D2u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) Fis uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions ont...