Ground States of Nonlinear Schrödinger-Kirchhoff Type Equation

Nonlinear Perturbations of the Kirchhoff Equation

In this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation u′′ −M(t, ‖u(t)‖)∆u+ |u| = f in Ω× (0, T0), u = 0 on Γ0×]0, T0[, ∂u ∂ν + δh(u′) = 0 on Γ1×]0, T0[, where Ω is a bounded domain of Rn with its boundary constiting of two disjoint parts Γ0 and Γ1; ρ > 1 is a real number; ν(x) is the exterior unit normal vector...

Ground states of dispersion-managed nonlinear Schrodinger equation

An exact pulse for the parametrically forced nonlinear Schrodinger equation (NLS) is isolated. The equation governs wave envelope propagation in dispersion-managed fiber lines with positive residual dispersion. The pulse is obtained as a ground state of an averaged variational principle associated with the equation governing pulse dynamics. The solutions of the averaged and original equations a...

The Nonlinear Schrödinger Equation Ground States on Product Spaces

Study of a nonlinear Kirchhoff equation with non-homogeneous material

In this paper we study a non-homogeneous elliptic Kirchhoff equation with nonlinear reaction term. We analyze the existence and uniqueness of positive solution. The main novelty is the inclusion of non-homogeneous term making the problem without a variational structure. We use mainly bifurcation arguments to get the results.

Remarks on Nonlinear Biharmonic Evolution Equation of Kirchhoff Type in Noncylindrical Domain

motivated by the problem of vertical flexion of fully clamped beams. Our main goal in this paper is to study the properties previously mentioned when the set D is a time-dependent nonempty bounded subset Ωt of Rn, which means that the supports of the extremes of the beam have small displacements. Note that the sets Ωt , where u=u(x,t) is defined, change with the time, which yields a noncylindri...