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| Entire Solutions for Certain Class of Non-linear General Difference Equations |
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| KeyWord:Non-linear difference equations, meromorphic function, entire solution, Nevanlinna theory |
| Author Name | Affiliation | | Harina P. Waghamore | Department of Mathematics, Bangalore University, Jnanabharathi Campus, Bengaluru 560056, Karnataka, India | | Manjunath B. E. | Department of Mathematics, Bangalore University, Jnanabharathi Campus, Bengaluru 560056, Karnataka, India |
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| Abstract: |
| In this paper, we investigate the entire solutions for a certain class of non-linear difference equations of the form: $f^n+q(z)e^{Q(z)}\mathcal{L}_1(z,f)=\alpha_1(z)e^{\beta_1(z)}+\alpha_2(z)e^{\beta_2(z)},$ where $\mathcal{L}_1(z,f)$ is the generalized linear difference operator, $\alpha_1(z)$ and $\alpha_2(z)$ are non-zero small functions of $f$, $q(z)$ and $Q(z)$(non-constant), $\beta_1(z)$ and $\beta_2(z)$ are non-zero polynomials. Our results improve upon and generalize some previously established findings. |
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