J. Nonl. Mod. Anal., 7 (2025), pp. 1240-1253.
Published online: 2025-07
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In this paper, we investigate the entire solutions for a certain class of non-linear difference equations of the form: $f^n+ q(z)e^{Q(z)}\mathcal{L}_1(z, f)$ $= α_1(z)e^{β_1(z)}+α_2(z)e^{ β_2(z)},$ where $\mathcal{L}_1(z, f)$ is the generalized linear difference operator, $α_1(z)$ and $α_2(z)$ are non-zero small functions of $f,$ $q(z)$ and $Q(z)$(nonconstant), $β_1(z)$ and $β_2(z)$ are non-zero polynomials. Our results improve upon and generalize some previously established findings.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1240}, url = {http://global-sci.org/intro/article_detail/jnma/24233.html} }In this paper, we investigate the entire solutions for a certain class of non-linear difference equations of the form: $f^n+ q(z)e^{Q(z)}\mathcal{L}_1(z, f)$ $= α_1(z)e^{β_1(z)}+α_2(z)e^{ β_2(z)},$ where $\mathcal{L}_1(z, f)$ is the generalized linear difference operator, $α_1(z)$ and $α_2(z)$ are non-zero small functions of $f,$ $q(z)$ and $Q(z)$(nonconstant), $β_1(z)$ and $β_2(z)$ are non-zero polynomials. Our results improve upon and generalize some previously established findings.