Oscillatory solutions of the equation y′(x) = m(x)y(x − n(x))

Monotonicity Properties of Oscillatory Solutions of Differential Equation

We obtain monotonicity results concerning the oscillatory solutions of the differential equation (a(t)|y′|p−1y′)′+f(t, y, y′) = 0. The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.

Higher-Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation

This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique. The equivalent deterministic equations are derived for each order and correction. The solution ensemble average and vari...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Analytical solutions for the fractional Fisher's equation

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...

Decay estimates of solutions to the IBq equation

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...