Strong maximum principle for non-linear parabolic differential-functional inequalities

Strong maximum principles for implicit parabolic functional-differential problems together with nonlocal inequalities with functionals

“…The results obtained are a generalization of some results given by J. Chabrowski [5], R. Redheffer and W. Walter [7], J. Szarski [8,9], P. Besala [1], W. Walter [10], N. Yoshida [11], the author [3,4], and are based on those results.…”

Estimate of solutions for differential and difference functional equations with applications to difference methods

“…A lot of equations of type (1.3) with the polynomial right-hand sides is described in [1,6,8,17] [6,17]. The results concerning differential or difference functional inequalities and numerical methods appearing in the papers by Besala and Paszek [2], Malec and Rosati [12,15], Pao [19], Redheffer and Walter [20,24], Szarski [22,23] and numerous others do not apply to nonlinear equations with such a general functional dependence as in our paper.…”

The Hadamard three-circles theorems for nonlinear equations

“…If inequality (iii) is satisfied in B rather than in A and if the strong maximum applies then M is strictly increasing. Strong maximum principles for nonlinear elliptic and parabolic equations and inequalities were established in [1], [3], [5] and [7]. Generally, (v) is an extra assumption; however this assumption is also needed in the linear case.…”