Related papers: On meromorphic solutions of Malmquist type differe…
The paper discusses a holomorphic nonlinear singular partial differential equation $(t \partial_t)^mu=F(t,x,\{(t \partial_t)^j \partial_x^{\alpha}u \}_{j+\alpha \leq m, j<m})$ under the assumption that the equation is of nonlinear totally…
In this article, we construct explicit meromorphic solutions of first order linear $q$-difference equations in the complex domain and we describe the location of all their zeros and poles. The homogeneous case leans on the study of four…
In this paper we shall study differential equations in the complex domain. The method of indeterminate coefficients and the majorant method lead to a proof of the existence and uniqueness of meromorphic solution of differential equations.…
A class of differential Riccati equations (DREs) is considered whereby the evolution of any solution can be identified with the propagation of a value function of a corresponding optimal control problem arising in L2-gain analysis. By…
We study the existence of solutions of the non-linear differential equations on the compact Riemannian manifolds $(M^n,g), n\geq 2$, \Delta_p u + a(x)u^{p-1} = \lambda f(u,x), (E2) where $\Delta_p$ is the $p-$laplacian, with $1<p<n$. The…
This paper shows that the nonlinear periodic eigenvalue problem $${cases} -\Delta u + V(x) u - f(x,u) = \lambda u, u \in H^1(\IR^N), {cases}$$ has a nontrivial branch of solutions emanating from the upper bound of every spectral gap of…
The aim of this paper is to study the problem of existence of remotely almost periodic solutions for the scalar differential equation $x'=f(t,x),$ where $f:\mathbb R\times \mathbb R\to \mathbb R$ is a continuous, monotone in $x$ and…
In the first part of the article we develop a comparison method for positive solutions of the semilinear Dirichlet problem $\Delta u+f(u)=0$ on domains $\Omega\subset \mathcal M^n$ of a Riemannian manifold $(\mathcal{M}^n,g)$ with a Ricci…
In this paper, we investigate positive solutions to a class of Laplace equations with a gradient term on a complete, connected, and noncompact Riemannian manifold \((M^n,g)\) with nonnegative Ricci curvature, namely \[-\Delta u =…
In this paper we have studied the growth of meromorphic solutions of higher order homogeneous and non-homogeneous linear difference equations with entire and meromorphic coefficients. We have extended and improved some results of Zhou and…
The main objective of this article is to discuss the local existence of the solution to an initial value problem involving a non-linear differential equation in the sense of Riemann-Liouville fractional derivative of order $\sigma\in(1,2),$…
The functional equations $ f^2+g^2=1 $ and $ f^2+2\alpha fg+g^2=1 $ are respectively called Fermat-type binomial and trinomial equations. It is of interest to know about the existence and form of the solutions of general quadratic…
This paper is devoted to a nonlinear singular Riemann-Liouville type fractional differential equation, the local existence of whose continuous solutions under the weakest condition remained as an open problem until now. The singularity of…
In this article, we deal with the order of growth of solutions of non-homogeneous linear differential-difference equation \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F(z), \end{equation*} where $A_{ij},$ $F\left(…
This chapter is mainly a tutorial introduction to methods recently developed in order to find all (as opposed to some) meromorphic particular solutions of given nonintegrable, autonomous, algebraic ordinary differential equations of any…
We consider in this paper the nonlinear elliptic equation with Neumann boundary condition \begin{align*} \begin{cases} \Delta u=a|u|^{m-1}u\,\,\mbox{ in }\,\,\rnp\\ \dfrac{\partial u}{\partial t}=b|u|^{\eta-1}u+f\,\,\mbox{ on…
Consider a differential system of the form $$ x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon), $$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times…
We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the…
We extend Halphen's theorem which characterizes the solutions of certain $n$th-order differential equations with rational coefficients and meromorphic fundamental systems to a first-order $n \times n$ system of differential equations. As an…
In this paper, we establish a general second main theorem for meromorphic mappings from $\mathbb C^m$ into a subvariety $V$ of $\mathbb P^n(\mathbb C)$ with respect to an arbitrary family of slowly moving hypersurfaces $\mathcal…