On the nonexistence of entire solutions of certain type of nonlinear differential equations

By Ping Li, Ajweezi. aljali. 2006

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Abstract By utilizing Nevanlinna's value distribution theory of meromorphic functions, it is shown that the following type of nonlinear differential equations: f n ( z ) + P n − 3 ( f ) = p 1 e α 1 z + p 2 e α 2 z has no nonconstant entire solutions, where n is an integer ⩾4, p 1 and p 2 are two polynomials ( ≢ 0 ) , α 1 , α 2 are two nonzero constants with α 1 / α 2 ≠ rational number, and P n − 3 ( f ) denotes a differential polynomial in f and its derivatives (with polynomials in z as the coefficients) of degree no greater than n − 3 . It is conjectured that the conclusion remains to be valid when P n − 3 ( f ) is replaced by P n − 1 ( f ) or P n − 2 ( f ) .

Subfields: Applied Mathematics

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