In the present work, we consider existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schrödinger equation with both fourth second-order dispersion terms. We first give criterion for single solution in terms coefficients terms, then show that discrete family exists which is characterized by distances between individual pulses. reduce problem these multi-pulses ...

Structure-preserving finite-difference schemes for general nonlinear fourth-order parabolic equations on the one-dimensional torus are derived. Examples include thin-film and Derrida–Lebowitz–Speer–Spohn equations. The conserve mass dissipate entropy. scheme associated to logarithmic entropy also preserves positivity. idea of derivation is reformulate in such a way ...

Numerical schemes are presented for a class of fourth order diffusion problems. These problems arise in lubrication theory for thin films of viscous fluids on surfaces. The equations being in general fourth order degenerate parabolic, additional singular terms of second order may occur to model effects of gravity, molecular interactions or thermocapillarity. Furthermore, we incorporate nonlinea...

Some new criteria for the oscillation of the fourth order functional differential equation d dt ( 1 a3(t) ( d dt 1 a2(t) ( d dt 1 a1(t) ( d dt x(t) )α1)α2)α3) + δq(t) f (x[g(t)]) = 0, where δ = ±1 are established. c © 2006 Elsevier Ltd. All rights reserved.

By a solution of () we mean a function x ∈ C[Tx,∞), Tx ≥ , which satisfies () on [Tx,∞). A solution is said to be nonoscillatory if x(t) =  for large t; otherwise, it is said to be oscillatory. Observe that if λ≥ , according to [, Theorem .], all nontrivial solutions of () satisfy sup{|x(t)| : t ≥ T} >  for T ≥ Tx, on the contrary to the case λ < , when nontrivial solutions satisfy...

Abstract. A nonlinear fourth-order parabolic equation with nonhomogeneous Dirichlet–Neumann boundary conditions in one space dimension is analyzed. This equation appears, for instance, in quantum semiconductor modeling. The existence and uniqueness of strictly positive classical solutions to the stationary problem are shown. Furthermore, the existence of global nonnegative weak solutions to the...