In this article, we obtain oscillation conditions for second-order differential equation with neutral term. Our results extend, improve, and simplify some known delay equations. Several effective illustrative implementations are provided.

All generators of the optimal algebra associated with a generalization Endem-Fowler equation are showed; some them allow to give invariant solutions. Variational symmetries and respective conservation laws also showed. Finally, representation Lie symmetry is showed by groups matrices.

We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ R is a smooth bounded domain and a is a positive smooth function. We study here the phenomenon of boundary bubbling solutions which do not exist for the isotropic case a ≡ constant. We determine the localization and asymptotic behavior of the boundary bubbles, and construct some bound...

In this paper, we will establish some new oscillation criteria for the second-order superlinear neutral delay dynamic equation of Emden-Fowler type [ a(t)(y(t) + r(t)y(τ(t))) ]∆ + p(t) |y(δ(t))| signy(δ(t)) = 0, on a time scale T; here γ > 1, a(t), r(t), τ(t), p(t) and δ(t)real-valued positive functions defined on T. Our results in the special case when T = R, improve the oscillation results fo...

/2 ( ) ( ) u u        where  is the Fourier transformation and  its inverse. The question is to determine for which values of the exponents pi and qi the only nonnegative solution (u, v) of (1) and (2) is trivial, i.e., (u; v) = (0, 0). When 2   , is the case of the Emden-Fowler equation 0 , 0     u u u k in N  (5) When ) 3 )( 2 /( ) 2 ( 1      N N N k , it has been prove...