- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Some results on meromorphic solutions of certain nonlinear differential equations Bull. Korean Math. Soc.Published online November 26, 2019 Nan Li and Lianzhong Yang Qilu Normal University, Shandong University Abstract : In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^{n}f^{(k)}+Q_{d_{*}}(z,f)=R(z)e^{\alpha(z)}$ and $f^{n}f^{(k)}+Q_{d}(z,f)=p_{1}(z)e^{\alpha_{1}(z)}+p_{2}(z)e^{\alpha_{2}(z)}$, where $Q_{d_{*}}(z,f)$ and $Q_{d}(z,f)$ are differential polynomials in $f$ with small functions as coefficients, of degree $d_{*}\, (\leq n-1)$ and $d\, (\leq n-2)$ respectively, $R,\, p_{1},\, p_{2}$ are non-vanishing small functions of $f$, and $\alpha,\, \alpha_{1},\, \alpha_{2}$ are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations. Keywords : Meromorphic functions; nonlinear differential equations; small functions; differential polynomials. MSC numbers : 34M05; 30D30; 30D35 Full-Text :