Oscillation Result for Some Non-homogeneous Linear Differential Equations and Its Application

This paper investigates solutions of some non-homogeneous linear differential equations, which have non-homogeneous term as the small function of solution. Using the similar method, we can generalize the result of G.Gundersen and L.Z.Yang.     

Controllability for Semilinear Functional and Neutral Functional Evolution Equations with Infinite Delay in Fréchet Spaces

The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Fréchet spaces, combined with the semigroup theory.     

Existence and Uniqueness of Solutions for two Classes of Functional Equations Arising in Dynamic Programming

In this paper we establish the existence,uniqueness and iterative approximation of solutions fortwo classes of functional equations arising in dynamic programming of multistage decision processes.The resultspresented here extend,and unify the corresponding results due to Bellman,Bhakta and Choudhury,Bhaktaand Mitra,Liu and others.     

μ-Pseudo Almost Periodic and Automorphic Solutions in the α-Norm for Some Partial Functional Differential Equations

In this work, we prove the existence and uniqueness of μ-pseudo almost periodic and μ-pseudo almost automorphic solutions in the α ?norm for some classes of partial differential equations in Banach spaces. For illustration, we study some models arising in physical systems.     

Strichartz Estimates for Schr(?)dinger Equations with Non-degenerate Coefficients

In the present paper,the full range Strichartz estimates for homogeneous Schr(?)dinger equations with non-degenerate and non-smooth coefficients are proved.For inhomogeneous equation,the non-endpoint Strichartz estimates are also obtained.     

Controllability results for functional semilinear differential inclusions in Fréchet spaces

In this paper, a recent nonlinear alternative for multivalued admissible contractions in Fréchet spaces due to Frigon combined with semigroups theory is used to investigate the controllability of some classes of semilinear functional and neutral functional differential inclusions in Fréchet spaces.     

Some results on semilinear stochastic differential equations in hilbert spaces

We study a semilinear stochastic equation by reducing it to a deterministic problem     

Controllability of stochastic semilinear functional differential equations in Hilbert spaces

In this paper approximate and exact controllability for semilinear stochastic functional differential equations in Hilbert spaces is studied. Sufficient conditions are established for each of these types of controllability. The results are obtained by using the Banach fixed point theorem. Applications to stochastic heat equation are given.     

New uniqueness results for fractional differential equations

We develop the Krasnoselskii–Krein type of uniqueness theorem for an initial value problem of the Riemann–Liouville type fractional differential equation which involves a function of the form f?(t,?x(t),?D ^q?1 x(t)), for 1<q<2 and establish the convergence of successive approximations. We prove a few other uniqueness theorems.     

Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces

In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results.     

Existence of multiple positive periodic solutions for functional differential equations

In our paper, by employing Krasnoselskii fixed point theorem, we investigate the existence of multiple positive periodic solutions for functional differential equations

     

Approximate controllability of semilinear functional equations in Hilbert spaces

In this paper approximate and complete controllability for semilinear functional differential systems is studied in Hilbert spaces. Sufficient conditions are established for each of these types of controllability. The results address the limitation that linear systems in infinite-dimensional spaces with compact semigroup cannot be completely controllable. The conditions are obtained by using the Schauder fixed point theorem when the semigroup is compact and the Banach fixed point theorem when the semigroup is not compact.     

New existence results of positive solution for a class of nonlinear fractional differential equations

In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.     

Unique existence results and numerical solutions for fourth-order impulsive differential equations with nonlinear boundary conditions

The work is concerned with three kinds of fourth-order impulsive differential equations with nonlinear boundary conditions. We at first focused on studying the existence and uniqueness of positive solutions for these kinds of problems. By converting the problem to an equivalent integral equation, then applying the new class of fixed point theorems for the sum operator on cone, we obtain the sufficient conditions which not only guarantee the existence of a unique positive solution, but also be applied to construct two iterative sequences for approximating it. Further, we present the numerical methods for solving the fourth-order differential equations. At last, some examples are given with numerical verifications to illustrate the main results.     

On Lipschitz conditions for ordinary differential equations in Fréchet spaces

We will give an existence and uniqueness theorem for ordinary differential equations in Fréchet spaces using Lipschitz conditions formulated with a generalized distance and row-finite matrices.