* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the fo...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

A generalized Nash equilibrium problem (GNEP) is formulated in which, in addition to pointwise constraints on both the control and state variables, the feasible sets are partially governed by the solutions of a linear elliptic partial differential equation. The decisions (optimal controls) of the players arise in their competitors optimization problems via the righthand side of the partial diff...

We introduce a concept of a fractional derivatives series and prove that any linear partial differential equation in two independent variables has a fractional derivatives series solution with coefficients from a differentially closed field of zero characteristic. The obtained results are extended from a single equation to D-modules having infinitedimensional space of solutions (i.e., non-holon...