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### Accelero-summation of the formal solutions of nonlinear difference equations

Annales de l’institut Fourier

In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level ${1}^{+}$”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...

### Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1

Annales Polonici Mathematici

For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where $X\left(x,y\right)=\lambda ₁x+\mu y+{\sum }_{i+j\ge 2}{c}_{ij}{x}^{i}{y}^{j}$, $Y\left(x,y\right)=\lambda ₂y+{\sum }_{i+j\ge 2}{d}_{ij}{x}^{i}{y}^{j}$ satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂| ≠ 1" or "μ...

### Analytic Solutions of second order Nonlinear Difference Equations all of whose Eigenvalues are 1

Rendiconti del Seminario Matematico della Università di Padova

### Entire solutions of q-difference equations and value distribution of q-difference polynomials

Annales Polonici Mathematici

We investigate the existence and uniqueness of entire solutions of order zero of the nonlinear q-difference equation of the form fⁿ(z) + L(z) = p(z), where p(z) is a polynomial and L(z) is a linear differential-q-difference polynomial of f with small growth coefficients. We also study the zeros distribution of some special type of q-difference polynomials.

### Further extending results of some classes of complex difference and functional equations.

Advances in Difference Equations [electronic only]

### Some properties of solutions of complex q-shift difference equations

Annales Polonici Mathematici

Combining difference and q-difference equations, we study the properties of meromorphic solutions of q-shift difference equations from the point of view of value distribution. We obtain lower bounds for the Nevanlinna lower order for meromorphic solutions of such equations. Our results improve and extend previous theorems by Zheng and Chen and by Liu and Qi. Some examples are also given to illustrate our results.

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