Growth of solutions of three order differential equations (Q1775274)

The author obtains two results that essentially extend the results of Chen, Gundersen and Frei. Let \(h_1, h_2\) be nonzero entire functions with \(\sigma(h_j)<1\), \(j=1,2\), \(h_0\) be a nonconstant polynomial. If \(F\) is an entire function with \(\sigma(F)<1\),then every nonconstant solution of \[ f'''+h_2e^{-z}f''+h_1e^zf'+h_0f=F \] has infinite order. If \(F\) is transcendental or \(F\equiv 0\), then every nonzero solution has infinite order. If \(h_1, h_2\) are nonzero polynomials then every nonzero solution has infinite order and \(\sigma_2(f)=1\). If \(F\) is transcendental or \(F\equiv 0\), then every nonzero solution has infinite order and \(\sigma_2(f)=1\).