By the use of functional modelling the products embodying physical solutions of identical function structures are recognized.
Many authors have investigated the existence solutions of fractional function equations with impulse [13 18].
In this paper, we seek all the optimal solutions of nonlinear function, including local optimal solutions and global optimal solutions.
The basis of hypersingular boundary integral equation (HBIE) development is singular and hypersingular field solutions of kernel functions.
This work is motivated by the ever increasing demands for integrating iterative solutions of nonlinear functions into embedded control systems.
The exact solutions of stress functions in a series form are obtained by the method of image.
In Theorem A, we obtain the convergent subsequence of an approximate solutions sequence of approximate problems and the limit belongs to the set of solutions of objective functions.
The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of displacement functions.
These peaks are due to "mirror solutions" of modal functions for some depths when considering only mode excitation factor modulus (see Figure 14).
The analytical solutions of displacement functions were classified into four cases with respect to different types of complex parameters and different corresponding physical meanings.
