Almost automorphic mild solutions to some semi-linear abstract differential equations with deviated argument Article

Gal, CG. (2005). Almost automorphic mild solutions to some semi-linear abstract differential equations with deviated argument . 17(4), 391-396. 10.1216/jiea/1181075350

cited authors

  • Gal, CG

authors

abstract

  • We present an integral equation method for the solution of a class of nonlinear two-point boundary value problems. The method relies on the use of the Kumar-Sloan transformation and uses special orthogonal polynomials to efficiently implement a Galerkin method for the solution of the resulting nonlinear integral equation. Numerical examples show the rapid convergence for smooth solutions which is a consequence of approximation theorems of Jackson&In this paper we consider the semi-linear differential equation with deviated argument x'(t) = Ax(t) + f(t, x(t), x[α(x(t), t)]), t ε R, in a Banach space (X,|| ||), where A is the infinitesimal generator of a C0-semigroup satisfying some conditions of exponential stability. Under suitable conditions on the functions f and α we prove the existence and uniqueness of an almost automorphic mild solution to the equation. © 2005 Rocky Mountain Mathematics Consortium.

publication date

  • December 1, 2005

Digital Object Identifier (DOI)

start page

  • 391

end page

  • 396

volume

  • 17

issue

  • 4