and Applied Analysis 3 system. Secondly, do the solution operators for fractional evolution equations have the perturbation properties analogous to those for the C0-semigroup? For evolution equations of integer order, perturbation properties play a significant role in monotone iterative technique; see 24 . Our paper copes with the above difficulties, and the new features of this paper mainly in...

In this article, we study a class of mixed monotone operators with perturbations. Using a monotone iterative technique and the properties of cones, we show the existence and uniqueness for fixed points for such operators. As applications, we prove the existence and uniqueness of positive solutions for nonlinear integral equations of second-order on time scales. In particular, we do not assume t...

In this paper, a new algorithm for solving a class of variational inclusions involving H-monotone operators is considered in Hilbert spaces. We investigate a general iterative algorithm, which consists of a resolvent operator technique step followed by a suitable projection step. We prove the convergence of the algorithm for a maximal monotone operator without Lipschitz continuity. These result...

The monotone iterative technique is applied to a class of nonlinear first order integro-differential equations in Banach spaces. First a linear system with a “small” nonlinear perturbation is solved using Banach’s Contraction Principle and the technique of Green’s function. Then based upon a comparison result, the existence of minimal and maximal solutions is proved.

In this paper, we generalize our proposed earlier computing method [10-11] to solve hydrodynamic semiconductor device equations. For submicron MOSFET devices, we simulate their temperature distribution by solving carrier energy balance equation with adaptive computational technique. This robust method based on: (1) the finite volume (FV) discertization scheme; (2) the monotone iterative (MI) al...

In this paper, we consider the problem of finding a zero of difference of two monotone operators in Hilbert space. Using the resolvent operator technique, we establish the equivalence between the variational inclusions and the fixed point problems. This alternative equivalent formulation is used to suggest and analyze a two-step iterative method for solving the variational inclusions involving ...