Meromorphic solutions of two certain types of nonlinear differential equations

Abstract

We investigate the meromorphic solutions of two types of nonlinear differential equations of the form b f n + a f n − 1 f ′ + Q d ( f ) = u ( z ) e v ( z ) , n ≥ d + 2 , f n + f n − 1 f ′ + Q d ( f ) = P 1 ( z ) e α 1 + P 2 ( z ) e α 2 , n ≥ d + 3 , where a , b are constants with ( a , b ) ≠ ( 0 , 0 ) and n , d are positive integers, u , P 1 , P 2 are nonzero rational functions, v , α 1 , α 2 are nonconstant polynomials, and Q d ( f ) denotes a differential polynomial in f with rational functions as its coefficients. Our results improve some recent related results.