substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

The negative association between smoking and both Alzheimer's (AD) and Parkinson's (PD) diseases is a consistent epidemiologic finding. This observation has prompted many investigators to conclude that cigarette smoking must be "biologically protective" against AD and PD. Rather than suggesting some as-yet-undefined pathogenetic clue, however, this negative association more likely is indicative...

We apply techniques of symmetry group analysis in solving two systems of conservation laws: a model of two strictly hyperbolic conservation laws and a zero pressure gas dynamics model, which both have no global solution, but whose solution consists of singular shock waves. We show that these shock waves are solutions in the sense of 1-strong association. Also, we compute all projectable symmetr...