In this paper we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently estabilished by De Philippis and Figalli [14], to provide global in time existence of distributional solutions to the semigeostrophic equations on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed.

In this paper, the existence of a mild solution to Cauchy problem for impulsive semilinear second-order differential inclusion in Banach space is investigated case when nonlinear term also depends on first derivative. This purpose achieved by combining Kakutani fixed point theorem with approximation solvability method and weak topology. combination enables obtaining result under easily verifiab...

In this paper, we establish some new properties of (?,c)-periodic and asymptotically functions, then apply them to study the existence uniqueness mild solutions these types following semilinear fractional differential equations: (1) {cDt?u(t)=Au(t)+cDt??1f(t,u(t)),1<?<2,t?R,u(0)=0(1) (2) {cDt?u(t)=Au(t)+cDt??1f(t,u(t?h)),1<?<2,t,h?R+,u(0)=0(2) where cDt?(?)(1<?<2) stands for Caputo derivative A...

In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.

In this paper we characterize the existence and uniqueness of periodic solutions of inhomogeneous abstract delay equations and establish maximal regularity results for strong solutions. The conditions are obtained in terms of R-boundedness of linear operators determined by the equations and LFourier multipliers. Periodic mild solutions are also studied and characterized.

Abstract. This paper considers the timeand space-dependent linear Boltzmann equation with general boundary conditions in the case of inelastic (granular) collisions. First, in the (angular) cut-off case, mild L1-solutions are constructed as limits of the iterate functions and boundedness of higher velocity moments are discussed in the case of inverse power collisions forces. Then the problem of...