Differential and differential-difference inequalities related to mixed problems for first order partial differential-functional equations. (English) Zbl 0737.35133

This paper presents a new approach for the solution of differential and differential-difference inequalities for PDE. It is proposed a very general difference operator which is defined as a weighted value related to 2 points of the mesh and also a discrete version comparison theorem. Applications of the present results to convergence are also presented.


35R10 Partial functional-differential equations
35R45 Partial differential inequalities and systems of partial differential inequalities
35F20 Nonlinear first-order PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs