Harina P. Waghamore, Manjunath Banagere Erajikkappa
Abstract:
In this article, we investigate the entire solutions of the
non-linear differential-difference equation
$$
f^n(z) + \omega f^{n-1}(z)f'(z) + q(z)e^{Q(z)}\mathcal{D}(z,f)
= p_1(z)e^{\lambda z} + p_2(z)e^{-\lambda z},
$$
where \(\mathcal{D}(z,f) = \sum_{i=0}^k b_if^{(t_i)}(z+c_i) \not\equiv 0\),
with \(b_i, c_i \in \mathbb{C}\), \(t_i\) being non-negative integers,
\(c_0 = 0\), \(t_0 = 0\). Here, \(n\) is an integer, \(\lambda, p_1, p_2\) are
non-zero constants, \(\omega\) is a constant, and
\(q \not\equiv 0\), \(Q(z)\) are polynomials such that \(Q(z)\) is non-constant.
Our results improve upon and generalize some previously established
findings in this area.
Submitted June 18, 2024. Published January 4, 2025.
Math Subject Classifications: 39A32, 30D35.
Key Words: Non-linear difference-differential equations; entire solution; Nevanlinna theory.
DOI: 10.58997/ejde.2025.03
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Harina P. Waghamore Department of Mathematics Bangalore University Jnana Bharathi Campus Bangalore - 560 056, India email: harina@bub.ernet.in, harinapw@gmail.com |
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Manjunath Banagere Erajikkappa Department of Mathematics Bangalore University Jnana Bharathi Campus Bangalore - 560 056, India email: manjunathbe@bub.ernet.in, manjunathbebub@gmail.com |
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