Sentence examples for mild and classical from inspiring English sources

In [11], the author discussed the existence and uniqueness of mild and classical solutions for the impulsive semilinear differential evolution equation.

Nonlocal conditions were initiated by Byszewski [20] when he proved the existence and uniqueness of mild and classical solutions of nonlocal Cauchy problems.

In Section 4, we are concerned with the existence of mild and classical solutions of the inhomogeneous non-autonomous integro-differential equation (1.1 - 1.2 1.1 - 1.2

Also, Wang et al. [32] proved the existence and uniqueness of mild and classical solutions for the nonlocal Cauchy problem in the form (1.5).

Hernandez and O'Regan [8] introduced this new class of differential equations where the impulses are not instantaneous and they investigated the existence of mild and classical solutions.

This paper is devoted to the study of the existence of mild and classical solutions for initial value problems described as an abstract non-autonomous second order integro-differential equation in Banach spaces.

Byszewski [33] proved the existence of mild, strong, and classical solutions for the nonlocal Cauchy problem.

Byszewski and Lakshmikantham [18] showed the existence and uniqueness of mild solutions and classical solutions when f and g in (1.1) satisfy Lipschitz type conditions.

Byszewski and Lakshmikantham [13], Byszewski [14] obtained the existence and uniqueness of mild solutions and classical solutions in the case that Lipschitz-type conditions are satisfied.

Based on the method of semigroups, the existence and uniqueness of mild, strong and classical solutions of semilinear evolution equations were discussed by Pazy [1].

We also show that mild solutions can become strong and classical solutions under appropriate assumptions.