Smooth Solutions of a Nonhomogeneous Iterative Functional Differential Equation with Variable Coefficients

Smooth Solutions of a Class of Iterative Functional Differential Equations

and Applied Analysis 3 where i, j, and k are nonnegative integers. Let I be a closed interval in R. By induction, we may prove that x∗jk t Pjk ( x10 t , . . . , x1,j−1 t ; . . . ;xk0 t , . . . , xk,j−1 t ) , 1.11 βjk Pjk ⎛ ⎜⎝ j terms { }} { x′ ξ , . . . , x′ ξ ; . . . ; j terms { }} { x k ξ , . . . , x k ξ ⎞ ⎟⎠, 1.12 Hjk Pjk ⎛ ⎜⎝ j terms { }} { 1, . . . , 1; j terms { }} { M2, . . . ,M2; . . . ...

Exact Solutions to a Generalized BBM Equation with Variable Coefficients

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

The C1 Solutions of the Series-Like Iterative Equation with Variable Coefficients

where F is a given function, f is an unknown function, λi ∈ R i 1, 2, . . . , n , and f k 1, 2, . . . , n is the kth iterate of f, that is, f0 x x, f x f ◦ fk−1 x . The case of all constant λis was considered in 1–10 . In 2000, W. N. Zhang and J. A. Baker first discussed the continuous solutions of such an iterative equation with variable coefficients λi λi x which are all continuous in interva...

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

Remarks on Fundamental Solutions to Schrödinger Equation with Variable Coefficients