Related papers: Entire Solutions Of Certain Non-Linear Differentia…
We show a necessary and sufficient condition on the existence of finite order entire solutions of linear differential equations $$ f^{(n)}+a_{n-1}f^{(n-1)}+\cdots+a_1f'+a_0f=0,\eqno(+) $$ where $a_i$ are exponential sums for…
We consider transcendental entire functions of finite order for which the zeros and $1$-points are in disjoint sectors. Under suitable hypotheses on the sizes of these sectors we show that such functions must have a specific form, or that…
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
In this paper we study the existence of solutions to an isotropic differential inclusion.
In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.
The objective of this study is to ascertain the existence and forms of the finite order meromorphic and entire functions of several complex variables satisfying some certain Fermat-type partial differential-difference equations by…
In this paper, the exact solutions of certain non-linear differential equations defined on a fractal subset of the real line are presented. Particular attention is paid to the Riccati-type fractal differential equation, for which a…
In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
We have discussed the problem of finding the condition on coefficients of $f''+A(z)f'+B(z)f=0, \quad B(z)(\not \equiv 0)$ so that all non-trivial solutions are of infinite order. The hyper-order of these non-trivial solutions of infinite…
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel…
In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is…
In this work nonlinear pseudo-differential equations with the infinite number of derivatives are studied. These equations form a new class of equations which initially appeared in p-adic string theory. These equations are of much interest…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
We show that a linear differential equation whose coefficients are entire functions of completely regular growth may have an entire solution of finite order which is not of completely regular growth. This answers a question of Gol'dberg and…
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…
We utilise recent results about the transcendental solutions to Riccati differential equations to provide a comprehensive description of the nature of the transcendental solutions to algebraic first order differential equations of genus…
The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a…
Considering differential equation f''+A(z)f'+B(z)f=0, where A(z) and B(z) are entire complex functions, our results revolve around proving all non-trivial solutions are of infinite order taking various restrictions on coefficients A(z) and…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…