In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. the study of dynamical properties of such equations is of great importance in many areas. the autonomous difference equat...

It is well known that for laminated composite plates a Levy-type solution exists only for cross-ply and antisymmetric angle-ply laminates. Numerous investigators have used the Levy method to solve the governing equations of various equivalent single-layer plate theories. It is the intension of the present study to introduce a method for analytical solutions of laminated composite plates with ar...

ion over Structural Types (1) Now consider encapsulating the equations: bar = sigrel (u, y) where foo ⋄ (u, v ,w) foo ⋄ (w , u + x , v + y) The equations of the body of bar needs to be partitioned into • Local Equations: equations used to solve for the local variables • Interface Equations: equations contributed to the outside Type-Based Structural Analysis for Modular Systems of Equations – p....

The Levy-type analytical solution is employed for the problem of bending of cross-ply and antisymmetric angle-ply piezoelectric hybrid laminated plates with at least two simply supported opposite edges. The governing equations of equilibrium are derived in the framework of the first-order shear deformation plate theory. The equations are classified according to the crystallography type of piezo...

We prove that the modulational instability criterion of formal Whitham modulation theory agrees with spectral stability long-wavelength perturbations periodic traveling wave solutions to generalized equation. use standard WKB procedure derive a quasilinear system three equations, written in terms mass, momentum, and number solution. same quantities as parameters rigorous perturbation linearized...