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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

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Open Access Research Article

Solution of special cases of PDEs with homogeneous terms

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pp. 1663–1670Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2559XML
Received:
01 Nov 2025
Published Online:
27 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2559
Pages:
1663–1670

Abstract

This study seeks to derive complete solutions for certain classes of third-order linear partial differential equations with constant coefficients involving three independent variables, expressed in the general form: B1 Hppp + B2 Hppn + B3 Hpnn + B4 Hnnn + B5 Hppm + B6 Hpmm + B7 Hpnm + B8 Hnnm + B9 Hnmm + B10 Hmmm + B11 Hpp + B12 Hpn + B13 Hpm + B14 Hnn + B15 Hnm + B16 Hmm + B17 Hp + B18 Hn + B19 Hm + B20 H = 0. Based on this supposition, the above equation can be simplified to a third-degree nonlinear second-order ordinary differential equation with three free functions.

Keywords

Subject Classifications

35A0535C05

References

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[2] T. H. Abed, S. N. Ketab, and H. A. Mohamad, “Oscillation Criteria of Solutions of Third Order Neutral Integro-Differential Equations,” Iraqi Journal of Science, vol. 62, no.10, pp. 3642–3647 (2021).‏
[3] S. N. Ketab and B. W. Abdullah, “Oscillation of second order half linear neutral differential equations,” Journal of Interdisciplinary Mathematics, vol. 24, no. 7, pp. 1779–1785 (2021).‏
[4] S. N. Ketab and S. F. Raji, “Oscillation and nonoscillation criteria for second order half-linear neutral difference equations,” Journal of Interdisciplinary Mathematics, vol. 25, no. 5, pp. 1525–1533 (2022).‏
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[6] D. G. Raheem and S. N. Ketab, “Oscillation and Nonoscillation Criteria of Solution Fourth Order Linear Neutral Differential Equations,” in International Conference on Mathematical Modeling and Computational Science, pp. 245–253, Cham, Switzerland: Springer Nature (Jan. 2025).‏
[7] S. N. Ketab and B. W. Abdullah, “Asymptotic Behavior Criteria for Solutions of Second-Order Half-Linear Neutral Differential Equations,” in Journal of Physics: Conference Series, vol. 1963, no. 1, p. 012129 (Jul. 2021).‏

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