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We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has…
For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restriction, we have established that all non-trivial solutions are of infinite order. In…
Bagderina \cite{Bagderina2013} solved the equivalence problem for a family of scalar second-order ordinary differential equations (ODEs), with cubic nonlinearity in the first-order derivative, via point transformations. However, the…
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.
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…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
Symmetries of variational problems are considered as symmetries of vector bundle valued exterior differential systems. This approach is then applied to third order ordinary variational equations of motion of the semi-classical spinning…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.
We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point technique when the elliptic equations contain second order…
In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only conditions on the…
It is shown that large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems, can be solved by the method of order completion. The solutions obtained can be assimilated with Hausdorff…
Extensive work has been done on the group classification of systems of equations in the literature. This paper identifies the gap in the literature which concerns the group classification of systems of two autonomous nonlinear second-order…
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…
We obtain explicit formulas for the solutions of the system of second-order difference equations of the form $x_{n+ 1} = \frac{x_n y_{n-1}}{y_n (a_n + b_n x_n y_{n - 1})}, \quad y_{n+1} = \frac{x_{n - 1} y_n}{x_n (c_n+d_n x_{n-1} y_n)}$,…
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous…
Let $A$ be a transcendental entire function of finite order. We show that if the differential equation $w''+Aw=0$ has two linearly independent solutions with only real zeros, then the order of $A$ must be an odd integer or one half of an…
We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions…
We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…