On representations,inversions, and approximations of laplace transforms in banach spaces

The paper extend's some of the basic results of classical Laplace transform theory to the Laplace transform of bounded Bochner integrable functions and the Laplace-Stieltjes transform of Lipschitz continuous functions with values in a Banach space.     

A characterization of uniform continuity for Volterra equations in Hilbert spaces

We show that the norm continuity of the resolvent for a Volterra equation of scalar type is equivalent to the decay to zero of a holomorphic operator family along some imaginary axis.

     

Impulsive neutral functional differential equations in banach spaces

In this paper, a fixed point theorem due to Schaefer is used to investigate the existence of solutions for first and second order impulsive neutral functional differential equations in Banach spaces.     

Resolution of quadratic equations in banach spaces

A new convergence theorem is established for the super-Halley method. This method has, in general, order three, but when it is applied to quadratic equations, its order is four.     

Existence and uniqueness results for boundary value problems of higher order fractional integro-differential equations involving gronwall's inequality in banach spaces

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α ∈ (n-1,n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder's inequality, a suitable singular Gronwall's inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.     

Explicit and approximate solutions of second order elliptic differential equations in hilbert and banach spaces

An explicit closed-form solution for an abstract elliptic equation in Hilbert or Banach space is presented. Using this explicit representation we propose an approximation with the accuracy automatically depending on the smoothness of the initial data.     

Exact solutions and finite time stability for higher fractional-order differential equations with pure delay

We obtain the exact solutions to the higher fractional-order nonhomogeneous delayed differential equations with Caputo-type fractional derivative by using a set of newly defined generalized delayed Mittag-Leffler matrix functions. The Laplace transform and inductive construction are taken up as the major solving approaches. Thereafter, we consider some special cases and prove that the new exact solutions are suitable for the delayed differential equations with arbitrary order . Additionally, we propose some criteria on the finite time stability of the higher fractional-order delay differential equations. Finally, an illustrative example is presented to test the correctness of the theoretical results.     

A coupled system of integral equations in reflexive banach spaces

We present an existence theorem for at least one weak solution for a coupled system of integral equations of Volterra type in a reflexive Banach spaces relative to the weak topology.     

The existence of nonoscillatory solutions of higher order nonlinear neutral equations

In this work, we consider the existence of nonoscillatory solutions of variable coefficient higher order nonlinear neutral differential equations. Our results include as special cases some well-known results for linear and nonlinear equations of first, second and higher order. We use the Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.     

Periodic solutions for higher order differential equations with deviating argument

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for higher order differential equations with deviating argument . Some new results on the existence of periodic solutions of the equations are obtained. Meanwhile, an example is given to illustrate our results.     

Kostin-type criterion for abstract linear differential equations of arbitrary order in banach spaces

We consider linear differential equations with operator coefficients in a Banach space. We construct necessary and sufficient conditions for the well-posedness of the Cauchy problem for these equations of arbitrary order that are analogous to the Kostin conditions for incomplete equations of the second order.     

Anisotropic equations in weighted Sobolev spaces of higher order

We consider the strongly nonlinear boundary value problem,

一类高阶非线性中立型差分方程组非振动解的存在性

研究了一类高阶非线性中立型差分方程组非振动解的存在性.利用Banach空间的压缩映象原理,获得了该方程组存在非振动解的充分条件.     

Oscillations of higher order differential equations of neutral type

In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of nth order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.     

Hölder continuous solutions for second order integro-differential equations in banach spaces

We study Hlder continuous solutions for the second order integro-differential equations with infinite delay （P1）: u′′（t）+cu′（t）+∫t-∞β（t-s）u′（s）ds+∫t-∞γ（t-s）u（s）ds = Au（t）-∫t-∞δ（t-s）Au（s）ds + f（t）on the line R, where 0 < α < 1, A is a closed operator in a complex Banach space X, c ∈ C is a constant, f ∈ C^α（R,X） and β,γ,δ∈L¹（R+）.Under suitable assumptions on the kernels β, γ and δ, we completely characterize the C^α- well-posedness of （P₁） by using operator-valued C^α-Fourier multipliers.     

Linearized oscillations for higher order neutral differential equations

In this paper, the oscillation of certain nonlinear neutral differential equations has been studied with the help of the oscillation of associated linear neutral differential equations