We introduce and study a family of lattice equations which may be viewed either as strongly nonlinear discrete extension the Gardner equation, or non-convex variant Lotka-Volterra chain. Their deceptively simple form supports very rich complex solitary patterns. Some these patterns are also found in quasi-continuum rendition, but more intriguing ones, like interlaced pairs waves, waves reverse ...

A broad class of forces, P, is identified, for which the Abraham-Lorentz-Dirac (ALD) and Newton-like equations have solutions in common. Moreover, these do not present pre-acceleration or escape into infinity (runaway behavior). Any continuous piecewise force can be represented terms functions belonging to this P. It was also argued that set common both sets wider, it proved could formulated ge...

Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+ |x|p) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superli...