A potential representation for the subset of traveling solutions of nonlinear dis-persive evolution equations is introduced. The procedure involves a reduction of a third order partial differential equation to a first order ordinary differential equation. In this representation it can be shown that solitons and solutions with compact support only exist in systems with linear or quadratic disper...

We study a third-order partial differential equation in the form τuttt +αutt −cuxx −buxxt = 0, (1) that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures. In contrast with the current literature on the subject, we show that when the critical parameter γ := α − τc2 b is negative, the e...

in this work, byemploying the leggett-williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

Uncertain partial differential equation is a type of partial differential equation driven by Liu processes. This paper first provides two methods for solving the first order linear uncertain partial differential equation and the inverse uncertainty distribution of solution is discussed. Moreover, on the basis of the study of uncertainty theory and the propagation process of internet public opin...

If solutions of a non-linear differential equation are contained in solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say tha...

Article history: Received 20 November 2015 Received in revised form 8 March 2016 Accepted 25 March 2016 Available online 31 March 2016

The third order linear differential equation Ly = y'" + p2(t)y" + P\{i)y' + Po(')y = 0 is studied, where />,(/) are continuous real-valued and periodic of period 0. Various criteria are obtained which guarantee "partial" asymptotic stability or instability by means of effective bounds on the Floquet characteristic multipliers of Ly = 0.