Related papers: On the oscillatory integration of some ordinary di…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
New necessary and sufficient conditions are given for the quantization of a class of periodic second order non-homogeneous ordinary differential equations in the complex plane in this paper. The problem is studied from the viewpoint of…
Complex Wadati-type potentials of the form $V(x)=-w^2(x) + iw_x(x)$, where $w(x)$ is a real-valued function, are known to possess a number of intriguing features, unusual for generic non-Hermitian potentials. In the present work, we…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
We consider general nonlinear elliptic equations of the form \[ \operatorname{div}\, A(x,Du) = 0 \quad \text{in } \Omega, \] where $A:\Omega \times \mathbb R^n \to \mathbb R^n$ satisfies a quasi-isotropic $(p,q)$-growth condition, which is…
For the ordinary differential equation (ODE) $\dot{x}(t) = f(t,x)$, $x(0) = x_0$, $t\geq 0$, $x\in R^d$, assume $f$ to be at least continuous in $t$ and locally Lipshitz in $x$, and if necessary, several times continuously differentiable in…
By revisiting an asymptotic integration theory of nonlinear ordinary differential equations due to J.K. Hale and N. Onuchic [Contributions Differential Equations 2 (1963), 61--75], we improve and generalize several recent results in the…
This work presents two simple criteria for determining the oscillatory nature of solutions to second-order differential equations with deviated arguments. These criteria extend the (Leighton-Wintner)-type criteria established by G.Q. Wang…
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial…
In this paper, we consider a class of singular nonlinear first order partial differential equations $t(\partial u/\partial t)=F(t,x,u, \partial u/\partial x)$ with $(t,x) \in \mathbb{R} \times \mathbb{C}$ under the assumption that…
For a mixed (advanced--delay) differential equation with variable delays and coefficients $$ \dot{x}(t) \pm a(t)x(g(t)) \mp b(t)x(h(t)) = 0, t\geq t_0 $$ where $$ a(t)\geq 0, b(t)\geq 0, g(t)\leq t, h(t)\geq t $$ explicit nonoscillation…
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…
We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in…
The Riccati equation method is used to establish Kamenev type conditions for the existence of oscillatory solutions to third order linear ordinary differential equations. Three oscillatory theorems are proved, which generalize the Lazer's…
The function exp(iwt) describes an oscillating motion. Energy of the oscillator is proportional to the square of w. exp(iwt) is the solution of a differential equation. We have replaced this differential equation by the corresponding…
It is well known that, contrary to the autonomous case, the stability/instability of solutions of nonautonomous linear ordinary differential equations $x' = A(t) x$ is in no relation to the sign of the real parts of the eigenvalues of…
The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations in the marginal, sub extremal and extremal cases.We show that the first of these criteria implies…
In this paper, we consider a generalized second order nonlinear ordinary differential equation of the form $\ddot{x}+(k_1x^q+k_2)\dot{x}+k_3x^{2q+1}+k_4x^{q+1}+\lambda_1x=0$, where $k_i$'s, $i=1,2,3,4$, $\lambda_1$ and $q$ are arbitrary…
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…
In this paper we study the dynamical behaviour of the differential equation \begin{equation*} x''+ax^+ -bx^-=f(t), \end{equation*} where $x^+=\max\{x,0\}$,\ $x^-=\max\{-x,0\}$, $a$ and $b$ are two different positive constants, $f(t)$ is a…