Some results of this paper improve and extend previous theorems given by Gao, and five examples are given to show the extension of solutions of the system of complex difference equations.
Theorems about the existence, uniqueness or extension of solutions of initial value problems, and about intersections of such solutions with barriers γ i can be found for example in [[35], Chapter 5].
Some results obtained in this paper improve and extend the previous theorems given by Gao, and five examples show the extension of solutions of the system of complex difference equation.
The integral equations are investigated with regard to the existence of a minimal and a maximal solution, extension of the solutions, and the generation of the solutions by successive approximations.
The proof uses the extension of a solution to an L2-type solution in a domain in CN×C, such that this extension satisfies the Cauchy Riemann equations.
Therefore, with the standard extension method of solution, we obtain for.
The approach suggested for the solution of this problem is based on the search for the solution with minimal Sobolev's norm (the most smooth solution), which provides, in particular, smooth extension of the solution to the area where no input data is available.
Also analytic and continuous extensions of solutions to homogeneous Dirac equations are studied, and it is shown that for each cell of harmonicity considered here there exist solutions to each iterate of the Dirac operator which may not be extended beyond any point of the closure of the cell.
The goal of this study is to identify the unknown boundary condition u ( 1, t ) at x = 1 by using the over measured data u ( x 0, t ) = ψ 1 and u x ( x 0, t ) = ψ 2. The key point here is the unique extensions of solutions on [ 0, x 0 ] to the closed interval [ 0, 1 ] which are implied by the uniqueness of the solutions.
Similar to the proof of Theorem in [4], we can prove that, which is the even extension of the solution of the initial boundary value problem (1.1)–(1.3) with initial value, is a periodic solution of the problem (1.1 - 1.2 1.1 - 1.2
