The existence of meromorphic solutions for two nonlinear complex delay-differential equations
This paper studied the existence of meromorphic solutions to two nonlinear complex delay-differential equations fn+n∑j=1ωjfn-j(f')j+q(z)eQ(z)f(k)(z+c)=p1(z)eλz+p2(z)e-λz,and fn+∑ωjfn-j(f')j+(q)(z)eQ(z)f(k)(z+c)=u(z)ev(z),where n ≥2,k ≥0 are positive integers,c,λ ≠0 are constants,ωj(j=1,,n)are constants such that ωj(j=1,…,n)are not all zero,q(z),pi(z)(i=1,2)are non-vanishing rational f unctions,Q(z),v(z)are non-constant polynomials,q(z),u(z)are non-vanishing meromorphic functions with order less than 1.Furthermore,investigated the form of existence and growth of the solutions.Our results improved and generalized some previous results.Some examples were given.
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