We prove an existence and uniqueness result for a Monge-Ampère type equation in the Cegrell class Eχ.

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...

in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasigeostrophic equation whose well-posedness is well-known, there ...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

The quasigeostrophic model is a simpli ed geophysical uid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasigeostrophic equation whose well-posedness is well-known, there see...