Related papers: Standard solutions of complex differential equatio…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3 and with rational functions as coefficients, also has…
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
A system of linear equations is said underdetermined when there are more unknowns than equations. Such systems may have infinitely many solutions. In this case, it is important to single out solutions possessing special features. A well…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
The objective of this paper is to investigate the existence and the forms of the pair of finite order entire and meromorphic solutions of some certain systems of Fermat-type partial differential-difference equations of several complex…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
In this paper, we consider the behaviour, when $q$ goes to $1$, of the set of a convenient basis of meromorphic solutions of a family of linear $q$-difference equations. In particular, we show that, under convenient assumptions, such basis…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
An approach is proposed for bounding the number of zeros that solutions of linear differential systems with polynomial coefficients may have. A bound is obtained in a special case which improves upon currently existing.
Using a new metric for generating rotating solutions, we derive in a general fashion the solution of an imperfect fluid and that of its conformal homolog. We discuss the conditions that the stress-energy tensors and invariant scalars be…
In the paper, we introduce a new type of unique range set for meromorphic function having deficient values which will improve all the previous result in this aspect.
In this paper we prove some normality criteria for a family of meromorphic functions, which involves the zeros of certain differential polynomials generated by the members of the family.
Meromorphic solutions of non-linear differential equations of the form $f^n+P(z,f)=h$ are investigated, where $n\geq 2$ is an integer, $h$ is a meromorphic function, and $P(z,f)$ is differential polynomial in $f$ and its derivatives with…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z+1)+w(z-1) = R(z,w(z)) (eqn 1) where R(z,w(z)) is rational in w(z) and meromorphic in z. Then either w(z) satisfies a difference linear or Riccati…
Solvability and smoothness of generalized solutions to boundary value problems for not self-adjoint differential-difference equations are studied. Necessary and sufficient conditions of Fredholmian solvability (with index zero) are…