[PDF] Top 20 Some results for fourth-order nonlinear differential equation with singularity

... Birkhoff twist theorem [–], topological degree theory [, ], Schauder’s fixed point the- orem [], the Krasnoselskii fixed point theorem in a cone [, ] and fixed point index theory [] have been employed to ... See full document

... published some results on third-order singular differential equation (see ...singular nonlinear third-order periodic boundary value ... See full document

... are some results on the Liénard equation with a singularity of repulsive type [14, 15, 19, ...Liénard equation with a repulsive ... See full document

... introduce some technical tools and present all the auxiliary results; in Section , by applying coincidence degree theory and some new inequalities, we obtain sufficient conditions for the existence of ... See full document

... differential equation (.), in which there are p-Laplacian and high-order cases, has not attracted much attention in the ...many results concerning the existence of a positive periodic solution for ... See full document

... x + a¨ x + b x ˙ + h(x) = p(t,x, ˙ x, ¨ x) (1.2) and established that the boundedness of both p(t) and p(τ)dτ together with the differ- entiability of the function h guaranteed the convergence of the solutions of the ... See full document

... ordinary differential equation that clearly determines whether the solutions are stable, bounded or periodic with- out actually going through the ... See full document

... Ordinary differential equations function we investigate the asymptotical stability and bounded ness of solution or 3rd order nonlinear differential ...interesting results related to the ... See full document

... Suppose that E is a Banach space which is partially ordered by a cone P ⊆ E, that is, x ≤ y if and only if y – x ∈ P. We denote the zero element of E by θ . A cone P is called normal if there exists a constant N >  ... See full document

... In what follows, we present some background details that motivate the study of this pa- per. Grace and Lalli [], Kirane and Rogovchenko [], Li and Agarwal [], Rogovchenko [], Rogovchenko and Tuncay [], and ... See full document

... on nonlinear elastic foun- dation which is no longer uniform in ...on nonlinear elastic foundation [10,15], most of them are concerned with the uniform foundation; that is, little is known about the ... See full document

... of nonlinear functional differential ...established some sufficient conditions for oscillation of all solutions of the second-order forced differential equation of the ... See full document

... We study vanishing at infinity solutions of a fourth-order nonlinear differential equation. We state sufficient and/or necessary conditions for the existence of the positive solution on the ... See full document

... higher- order nonlinear fractional differential equations with integral boundary ...The results are established by converting the problem into an equivalent integral equation and applying ... See full document

... determine whether or not the solution will blow up. Feng et al. study the Schrödinger equation with gain/loss in [] and []. They, respectively, give the limit behavior of so- lution as ε →  and the global ... See full document

... Asymptotic Behavior of olutlons of Fourth Order Nonlinear Differential Equations, Proc.. An Oscillation Criterion for a Fourth Order Integrally Superllnear Differential Equation, Attl.[r] ... See full document

... where f ∈ C([, ], R) and g ∈ C(R) are real functions. This kind of problem arises in the study of deflections of elastic beams on nonlinear elastic foundations. The problem has the following physical description: ... See full document

... establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time ...The results in this paper unify the oscillation of the second-order ... See full document

... a nonlinear fourth-order equation where the linear part is given by the second derivative of an invertible second-order ...The equation includes a deviating argument and the ... See full document

... of nonlinear evolution equations which arise in engineering sciences, mathematical physics and real time application ...the nonlinear partial differential equation, namely, the fourth ... See full document