We obtain the existence and uniqueness of Lp-solutions (1 ≤ p ≤ ∞) for Fokker–Planck equations with irregular and degenerate coefficients. Moreover, as an application, we also derive the existence and uniqueness of L1-solutions for the Fokker–Planck–Boltzmann equation.

In this article, we consider dynamic behaviours of a class of non-linear delay stochastic evolution equations. Local existence and uniqueness of the solutions are obtained with the aid of proper iterative scheme and moment estimations. We also propose a continuation result and our results generalize the known results.

In this article, we consider an optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in Hilbert spaces and the cost functional has a quadratic growth. The existence and uniqueness of the optimal control are obtained by the means of an associated backward stochastic differential equations with a quadratic growth and an unbounded terminal value. As an application, an optimal control of stochastic partial differential equations with dynamical boundary conditions is also given to illustrate our results.

In this paper, by using the fixed points of strict-set contractions, we study the existence of at least one or two positive solutions to the second-order three-point boundary value problem y''(t)+a(t)ƒ(y(t))=θ, 0<t<1, y(0)=θ, y(1)=βy(η) in Banach space E, where θ is the zero element of E, 0<β<1, 0<η<1 and a (t) is allowed to change sign on [0, 1]. As an application, we also give one example to demonstrate our results.

Pontryagin’s maximum principle for an optimal control system governed by an ordinary differential equation with endpoint constraints is proved under the assumption that the control domain has no linear structure. We also obtain the variational equation, adjoint equation and Hamilton system for our problem.