Recent zbMATH articles in MSC 34M10https://zbmath.org/atom/cc/34M102021-06-15T18:09:00+00:00WerkzeugGrowth of \(\phi \)-order solutions of linear differential equations with meromorphic coefficients on the complex plane.https://zbmath.org/1460.341082021-06-15T18:09:00+00:00"Kara, Mohamed Abdelhak"https://zbmath.org/authors/?q=ai:kara.mohamed-abdelhak"Belaïdi, Benharrat"https://zbmath.org/authors/?q=ai:belaidi.benharratIn this paper, the authors study the growth of higher order linear differential equations with meromorphic coefficients of \(\varphi\)-order on the comlpex plane. They prove many theorems by using the concepts of \(\varphi\)-order and \(\varphi\)-type. These theorems extend previous results due to Chyzhykov, Semochko, Belaïdi, Cao, Xu, Chen and Kinnunen. This work is interesting.
Reviewer: Karima Hamani (Mostaganem)Growth of solutions of complex differential equations in a sector of the unit disc.https://zbmath.org/1460.341072021-06-15T18:09:00+00:00"Belaïdi, Benharrat"https://zbmath.org/authors/?q=ai:belaidi.benharratIn the paper, the author discuss the growth of solutions of homogeneous linear complex differential equation by using the concept of lower $[p,q]$-order and lower $[p,q]$-type in a sector of the unit disc instead of the whole unit disc, and they obtain similar results as in the case of the unit disc.
Furthermore, they establish the concept of lower $[p,q]$-order and lower $[p,q]$-type of a meromorphic function in a sector $\Omega$ and extension of some earlier results in this area.
The work carried out here is no doubt a good piece of modern research work. Moreover, it contains a resourceful and current reference list at the end.
Reviewer: Nityagopal Biswas (Kalyani)Existence of transcendental meromorphic solutions on some types of nonlinear differential equations.https://zbmath.org/1460.341062021-06-15T18:09:00+00:00"Hu, Peichu"https://zbmath.org/authors/?q=ai:hu.peichu"Liu, Manli"https://zbmath.org/authors/?q=ai:liu.manliSummary: We show that when \(n>m\), the following delay differential equation \[f^n(z)f'(z)+p(z)(f(z+c)-f(z))^m=r(z)e^{q(z)}\] of rational coefficients \(p,r\) doesn't admit any transcendental entire solutions \(f(z)\) of finite order. Furthermore, we study the conditions of \(\alpha_1, \alpha_2\) that ensure existence of transcendental meromorphic solutions of the equation \[f^n(z) + f^{n-2}(z)f'(z)+ P_d(z,f)=p_1(z)e^{\alpha_1( z)}+p_2(z)e^{\alpha_2 (z)}.\] These results have improved some known theorems obtained most recently by other authors.