D. Bahuguna

Almost periodic solutions of neutral functional differential equations

In this paper we study a non-autonomous neutral functional differential equation in a Banach space. Applying the theory of semigroups of operators to evolution equations and Krasnoselskiis fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration.

APPROXIMATIONS OF SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS

The convergence of the Faedo-Galerkin approximation of solutions to a class of integro-differential equations of the type, considered in a separable Hilbert space H, is established where A is a closed, positive definite, self-adjoint linear operator from the domain D(A) ⊂ H into H such that D(A) is dense in H, f and g are nonlinear maps defined from [0, T] × X α(T) into H, X α(T) = C([0, T], D(A α)) for 0 < α < 1 is endowed with the supremum norm and the kernel a is in Lp (0, T) for some 1 < p < ∞.

A comparative study of numerical methods for solving an integro-differential equation

This paper is devoted to the numerical comparison of methods applied to solve an integro-differential equation. Four numerical methods are compared, namely, the Laplace decomposition method (LDM), the Wavelet-Galerkin method (WGM), the Laplace decomposition method with the Pade approximant (LD-PA) and the homotopy perturbation method (HPM).

Rothe’s method to parabolic integra-differential equations via abstract integra-differential equations

In this paper an abstract integrodiffe-rential equation associated with a singlevalued m-accretive operator is considered in a Banach space whose dual is uniformly convex. The existence and uniqueness of strong solution is proved with the help of Rothes method. The established results are then applied to assert the existence of unique strong solution of a class of parabolic initial boundary value problems with memory

Integrodifferential equations with analytic semigroups

In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

Common fixed point theorems in Menger spaces with common property (E.A)

In this paper, we introduce the notion of common property (E.A) in Menger spaces besides proving a result interrelating the property (E.A) with common property (E.A). Thereafter, using the common property (E.A), some common fixed point theorems are proved for self mappings in Menger spaces which include results involving quasi-contraction as well as @f-type contraction. Our results generalize several known results in Menger as well as metric spaces. Some related results are also derived besides furnishing an illustrative example.

Existence of solutions to Sobolev-type partial neutraldifferential equations

This work is concerned with a nonlocal partial neutral differential equation of Sobolev type. Specifically, existence of the solutions to the abstract formulations of such type of problems in a Banach space is established. The results are obtained by using Schauders fixed point theorem. Finally, an example is provided to illustrate the applications of the abstract results.

APPROXIMATION OF SOLUTIONS TO EVOLUTION INTEGRODIFFERENTIAL EQUATIONS

In this paper we study a class of evolution integrodifferential equations. We first prove the existence and uniqueness of solutions and then establish the convergence of Galerkin approximations to the solution.

Application of rothe’s method to nonlinear schrodinger type equations

The unique global existence of strong solution of a nonlinear Schrbdinger type equation is established by reformulating it as an abstract Cauchy problem posed in a real Hilbert space and applying Rothe1s method

Approximation of solutions to retarded differential equations with applications to population dynamics

We consider a retarded differential equation with applications to population dynamics. We establish the convergence of a finite-dimensional approximations of a unique solution, the existence and uniqueness of which are also proved in the process.