On Transcendental Meromorphic Solutions of a Certain Type of Nonlinear Complex Differential Equations

Zheng LI, Jun Fan CHEN

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 371-386.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 371-386. DOI: 10.12386/A2022sxxb0029

On Transcendental Meromorphic Solutions of a Certain Type of Nonlinear Complex Differential Equations

  • Zheng LI, Jun Fan CHEN
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Abstract

We study transcendental meromorphic solutions of a certain type of nonlinear complex differential equations f4+a(z)ff(k)=p1(z)eα1(z)+p2(z)eα2(z), where a, p1, p2 are non-zero rational functions and α1, α2 are nonconstant polynomials. Further, we can derive the conditions concerning the terms α1, α2, p1 and p2 that are necessary for the existence and the form of a transcendental meromorphic solution of the equation above. In addition, we analyze the existence of meromorphic solutions of another type of nonlinear complex differential equations f3+a(z)f=p1(z)eν(z)+p2(z)eν(z), where a, p1, p2 are non-zero rational functions and ν is a nonconstant polynomial. These results extend some known results obtained most recently.

Key words

Nevanlinna theory / meromorphic solutions / complex differential equations / zeros / poles

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Zheng LI, Jun Fan CHEN. On Transcendental Meromorphic Solutions of a Certain Type of Nonlinear Complex Differential Equations. Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 371-386 https://doi.org/10.12386/A2022sxxb0029

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